Quantum memory systems and quantum repeater systems comprising doped polycrystalline ceramic optical devices and methods of manufacturing the same

ABSTRACT

A quantum memory system includes a doped polycrystalline ceramic, a magnetic field generation unit, and one or more pump lasers. The doped polycrystalline ceramic is positioned within a magnetic field of the magnetic field generation unit when the magnetic field generation unit generates the magnetic field, the one or more pump lasers are optically coupled to the doped polycrystalline ceramic, and the doped polycrystalline ceramic is doped with a rare-earth element dopant that is uniformly distributed within a crystal lattice of the doped polycrystalline ceramic.

CROSS REFERENCE TO RELATED APPLICATIONS

This Application is a continuation of Int'l App. No. PCT/US17/32358filed May 12, 2017, which claims priority to U.S. App. Nos. 62/336,170,filed May 13, 2016, and 62/465,372, filed Mar. 1, 2017, each of which isincorporated by reference herein in its entirety.

BACKGROUND

The present disclosure relates to quantum memory systems and quantumrepeater systems. More specifically, the present disclosure introducestechnology for quantum memory systems and quantum repeater systemshaving a doped polycrystalline ceramic optical device.

BRIEF SUMMARY

According to the subject matter of the present disclosure, a quantummemory system includes a doped polycrystalline ceramic (called dopedpolycrystalline ceramic optical device infra; e.g. optical element,optics, optical component, assembly, structure), a magnetic fieldgeneration unit, and one or more pump lasers. The doped polycrystallineceramic optical device is positioned within a magnetic field of themagnetic field generation unit when the magnetic field generation unitgenerates the magnetic field, the one or more pump lasers are opticallycoupled to the doped polycrystalline ceramic optical device, and thedoped polycrystalline ceramic optical device is doped with a rare-earthelement dopant that is uniformly distributed within a crystal lattice ofthe doped polycrystalline ceramic optical device.

In accordance with one embodiment of the present disclosure, an opticalsystem includes a quantum repeater system, one or more magnetic fieldgeneration units, and one or more pump lasers. The quantum repeatersystem includes two doped polycrystalline ceramic optical devices andrepeater entanglement optics Each doped polycrystalline ceramic opticaldevice of the quantum repeater system is positioned within a magneticfield of the one or more magnetic field generation units when the one ormore magnetic field generation units generate the magnetic field. Eachdoped polycrystalline ceramic optical device of the quantum repeatersystem is doped with a rare-earth element dopant that is uniformlydistributed within a crystal lattice of the doped polycrystallineceramic optical device. At least one of the one or more pump lasers areoptically coupled to each doped polycrystalline ceramic optical deviceof the quantum repeater system. Further, the repeater entanglementoptics include two entangling pathways optically coupled to each dopedpolycrystalline ceramic optical device and a beamsplitter positionedsuch that each entangling pathway traverses the beamsplitter.

In accordance with another one embodiment of the present disclosure, amethod of manufacturing a doped polycrystalline ceramic optical deviceincludes mixing a plurality of transition metal complexes and aplurality of rare-earth metal complexes to form a metal salt solution,heating the metal salt solution to form a heated metal salt solution,mixing the heated metal salt solution and an organic precursor to inducea chemical reaction between the heated metal salt solution and theorganic precursor to produce a plurality of rare-earth dopednanoparticles, and sintering the plurality of rare-earth dopednanoparticles to form a doped polycrystalline ceramic optical devicehaving a rare-earth element dopant that is uniformly distributed withina crystal lattice of the doped polycrystalline ceramic optical device.

Although the concepts of the present disclosure are described hereinwith primary reference to some specific quantum memory systems, it iscontemplated that the concepts will enjoy applicability to quantummemory systems and quantum repeater systems having any configuration.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The following detailed description of specific embodiments of thepresent disclosure can be best understood when read in conjunction withthe following drawings, where like structure is indicated with likereference numerals and in which:

FIG. 1 is a schematic illustration of a quantum memory system having adoped polycrystalline ceramic optical device with a rare-earth elementdopant, according to one or more embodiments shown and described herein;

FIG. 2 is a schematic illustration of ground and excited energy statesof a superposition of a shaped spectral structure of the rare-earthelement dopant of FIG. 1, according to one or more embodiments shown anddescribed herein;

FIG. 3A is a schematic illustration of a precursor mixture used to formthe doped polycrystalline ceramic optical device of FIG. 1, according toone or more embodiments shown and described herein;

FIG. 3B is a schematic illustration of a plurality of rare-earth dopednanoparticles used to form the doped polycrystalline ceramic opticaldevice of FIG. 1, according to one or more embodiments shown anddescribed herein;

FIG. 3C is a schematic illustration of a metal salt mixture used to formthe doped polycrystalline ceramic optical device of FIG. 1, according toone or more embodiments shown and described herein;

FIG. 3D is a schematic illustration the addition of organic precursor toa heated metal salt mixture used to form the doped polycrystallineceramic optical device of FIG. 1, according to one or more embodimentsshown and described herein;

FIG. 3E is a schematic illustration of a plurality of rare-earth dopednanoparticles used to form the doped polycrystalline ceramic opticaldevice of FIG. 1, according to one or more embodiments shown anddescribed herein;

FIG. 4 is a schematic illustration of an optical system having multipledoped polycrystalline ceramic optical devices with a rare-earth elementdopant as depicted in FIG. 1, arranged in a quantum repeater system,according to one or more embodiments shown and described herein; and

FIG. 5 schematically depicts an example optical system comprisingmultiple quantum repeater systems, according to one or more embodimentsshown and described herein.

DETAILED DESCRIPTION

FIG. 1 is a schematic illustration of quantum memory system 100. Thequantum memory system 100 comprises a doped polycrystalline ceramicoptical device 120, a magnetic field generation unit 140, a storagephoton generator 170, and one or more pump lasers 180, for example afirst pump laser 180 a and a second pump laser 180 b. As describedbelow, the quantum memory system 100 is structurally configured to storeand release one or more storage photons, for example, on demand, suchthat the quantum memory system 100 may be synchronized with one or moreadditional quantum memory systems to form a quantum repeater system 201,for example, as depicted in FIG. 4. Further, the components of thequantum memory system 100, for example, the doped polycrystallineceramic optical device 120 may be positioned in an optical system 200that includes one or more quantum repeater systems 201 each comprising apair of doped polycrystalline ceramic optical devices 120, as depictedin FIG. 4. The optical system 200 including the one or more quantumrepeater systems 201 may be structurally configured to entangle a pairof storage photons that are each stored and released by the dopedpolycrystalline ceramic optical devices 120 of the respective quantummemory systems. Moreover, the quantum memory system 100 and the opticalsystem 200 described herein may be incorporated into one or more quantumcommunications systems, for example, quantum key generation systems,quantum telecommunications systems, quantum internet systems, and anyother current or yet-to be developed quantum communications systems.

As depicted in FIG. 1, the doped polycrystalline ceramic optical device120 of the quantum memory system 100 includes a crystal lattice 122 andis doped with a rare-earth element dopant 130 that is uniformlydistributed within the crystal lattice 122 of the doped polycrystallineceramic optical device 120. As used herein, “uniform distribution”refers to a distribution of a dopant within a crystal lattice, such asthe rare-earth element dopant 130, in which at least 50% of the dopantis doped into grains of the crystal lattice at locations apart from thegrain boundaries of the crystal lattice. The doped polycrystallineceramic optical device 120 comprises a first end 126 and a second end128, which may be opposite the first end 126. The doped polycrystallineceramic optical device 120 may comprise a metal oxide formed into apolycrystalline ceramic, such as yttrium oxide, zirconium oxide, hafniumoxide or the like. For example, the doped polycrystalline ceramicoptical device 120 may comprise a combination of yttrium oxide andzirconium oxide. As another example, the doped polycrystalline ceramicoptical device 120 may comprise a combination of zirconium oxide andhafnium oxide where hafnium oxide comprises about 2-10% of a totalmolecular weight of the doped polycrystalline ceramic optical device120, for example, 4%, 6%, 8%, or the like. Further, the dopedpolycrystalline ceramic optical device 120 may be transparent.

As depicted in FIG. 1 the doped polycrystalline ceramic optical device120 may comprise a doped polycrystalline ceramic optical waveguide 121having a polycrystalline ceramic core 125 and a cladding 127 surroundingthe polycrystalline ceramic core 125. The cladding 127 comprises arefractive index that is lower than a refractive index of thepolycrystalline ceramic core 125 such that photons traversing thepolycrystalline ceramic core 125 undergo total internal reflection atthe core-cladding boundary between polycrystalline ceramic core 125 andthe cladding 127. When the difference between the refractive indices ofthe polycrystalline ceramic core 125 and the cladding 127 is small, alarger polycrystalline ceramic core 125 (relative to the cladding 127)may be desired and when there the difference between the refractiveindices of the polycrystalline ceramic core 125 and the cladding 127 islarge, a smaller polycrystalline ceramic core 125 (relative to thecladding 127) may be desired.

Further, the polycrystalline ceramic core 125 may comprise a metaloxide, for example, yttrium oxide and/or zirconium oxide formed into apolycrystalline ceramic. Further, the cladding 127 may comprise apolymer, for example, a UV durable polymer, a polymer in an organicmatrix, or any other known or yet to be developed polymer suitable as acladding. As one example, the polycrystalline ceramic core 125 comprisesyttrium oxide and the cladding 127 comprises a polymer. Alternatively,the cladding 127 may comprise a polycrystalline ceramic for example, ametal oxide, for example, yttrium oxide and/or zirconium oxide formedinto a polycrystalline ceramic. As one example, the polycrystallineceramic core 125 may comprise a combination of yttrium oxide, andzirconium oxide and the cladding 127 may comprise yttrium oxide.Moreover, the polycrystalline ceramic core 125 of the dopedpolycrystalline ceramic optical waveguide 121 is doped with a rare-earthelement dopant 130 that is uniformly distributed within a crystallattice 122 of the polycrystalline ceramic core 125. Further, while thedoped polycrystalline ceramic optical device 120 is depicted as thedoped polycrystalline ceramic optical waveguide 121 in FIG. 1, it shouldbe understood that the doped polycrystalline ceramic optical device 120may comprise any optical device, for example, optical devices that donot include a core and a cladding.

Further, the doped polycrystalline ceramic optical device 120 maycomprise a variety of shapes and sizes to facilitate photon absorptionand release. For example, the doped polycrystalline ceramic opticaldevice 120 may comprise a length extending between the first end 126 andthe second end 128 that is between about 1 cm and about 50 cm, forexample, 5 cm, 10 cm, 15 cm, 20 cm, 30 cm, 40 cm, or the like. Further,the doped polycrystalline ceramic optical device 120 and may comprise across sectional area of between about 0.01 mm² and about 25 mm², forexample, about 0.1 mm², 0.5 mm², 1 mm², 2 mm², 5 mm², 10 mm², 15 mm², 20mm², or the like. Moreover, the doped polycrystalline ceramic opticaldevice 120 may comprise a width of between about 0.1 mm and 5 mm, suchas 0.5 mm, 0.75 mm, 1 mm, 2 mm, 3 mm, 4 mm, or the like, and a height ofbetween about 0.1 mm and about 5 mm, such as 0.5 mm, 0.75 mm, 1 mm, 2mm, 3 mm, 4 mm, or the like. The doped polycrystalline ceramic opticaldevice 120 may also comprise an optical cavity positioned within thedoped polycrystalline ceramic optical device 120. In operation, theoptical cavity may trap light, such as a storage photon, within theoptical cavity until the light is absorbed, for example, absorbed by therare-earth element dopant 130 located within.

The rare-earth element dopant 130 doped into the crystal lattice 122 ofthe doped polycrystalline ceramic optical device 120 includes one ormore rare-earth elements, for example, one or more lanthanide elements,including erbium, thulium, praseodymium, lanthanum, cerium, neodymium,samarium, europium, gadolinium, terbium, dysprosium, holmium, ytterbium,and lutetium, or the like, as well non-lanthanide elements such asscandium, and oxides of each of these lanthanide and non-lanthaniderare-earth elements. Further, the rare-earth element dopant 130 maycomprise between about 0.01% and about 2% of the total molecular weightof doped polycrystalline ceramic optical device 120, for example,0.025%, 0.05%, 0.075%, 0.1%, 0.125%, 0.15%, 0.2%, 0.25%, 0.5%, 0.75%,1.0%, 1.25%, 1.5%, 1.75%, or the like. As one example, the rare-earthelement dopant 130 comprises between about 0.05% to about 0.15% of atotal molecular weight of the doped polycrystalline ceramic opticaldevice 120.

The rare-earth element dopant 130 doped into the crystal lattice 122 ofthe doped polycrystalline ceramic optical device 120 may include ashaped spectral structure positioned within the rare-earth elementdopant 130, the shaped spectral structure comprising a superposition(e.g., of one or more electrons of the rare-earth element dopant 130)that is transferable between a plurality of energy states. For example,as explained in more detail below, one or more pump lasers 180 mayirradiate the doped polycrystalline ceramic optical device 120 togenerate the shaped spectral structure within the rare-earth elementdopant 130. In operation, the superposition of the shaped spectralstructure is transferrable between energy states, for example, when thedoped polycrystalline ceramic optical device 120 receives one or morestorage photons emitted by the storage photon generator 170 and/or oneor more pump pulses emitted by the one or more pump lasers 180, asdescribed in more detail below. In operation, ions of rare-earthelements have narrow 4f-4f transitions and have long optical coherence,which makes them suitable for transferring the superposition of theshaped spectral structure between energy states to store the storagephoton within the rare-earth element dopant 130. Moreover, the dopedpolycrystalline ceramic optical device 120 may also be doped withnon-rare-earth element dopants, such as oxides of Mg, Ca, Sc, Ti, V, Nb,Ta, Mo, W, Sn, and In.

Further, the doped polycrystalline ceramic optical device 120 may formedby sintering a plurality of rare-earth doped nanoparticles 110. Theplurality of rare-earth doped nanoparticles 110 may comprise Er³⁺ dopedY₂O₃ nanoparticles. The plurality of rare-earth doped nanoparticles 110may be formed my mixing a plurality of transition metal complexes 112, aplurality of rare-earth metal complexes 114, an organic precursor 116,and water, such as deionized water (FIGS. 3A-3E). For example, by dopingEr³⁺ ions into nanoparticles, such as, Y₂O₃ nanoparticles, using asolution phase synthesis (e.g., using the methods described below withrespect to FIGS. 3A-3E) the doped polycrystalline ceramic optical device120 formed by sintering these rare-earth doped nanoparticles 110 maycomprise atomically homogenously distributed rare earth ions (e.g., Er³⁺ions).

The plurality of transition metal complexes 112 may be metal salts suchas metal chlorides or metal nitrates, including zirconium salts, yttriumsalts or combinations thereof. Further, the plurality of rare-earthmetal complexes 114 may comprise metal complexes, for example, metalsalts, of any of the rare-earth elements described above. By usingrare-earth metal complexes 114 form the plurality of rare-earth dopednanoparticles 110 (e.g., diameters of 200 nm or less) the rare-earthelement dopant 130 positioned within resultant doped polycrystallineceramic optical device 120 may be more uniformly distributed within thecrystal lattice 122 of the doped polycrystalline ceramic optical device120, improving performance of the doped polycrystalline ceramic opticaldevice 120. Moreover, the organic precursor 116 may comprise urea,ammonium hydroxide, or the like.

Referring again to FIG. 1, the storage photon generator 170 is opticallycoupled to the doped polycrystalline ceramic optical device 120, forexample, to the first end 126 or the second end 128 of the dopedpolycrystalline ceramic optical device 120, and is structurallyconfigured to generate and emit a storage photon, for example, anentangled storage photon or a non-entangled storage photon. The storagephoton generator 170 comprises a photon source, for example, a laser, alaser optically coupled to a non-linear crystal, a parametric downconvertor, or the like. Further, the storage photon generator 170 maygenerate and emit storage photons using a four-wave mixing process, orany method or process of generating photons.

In operation, the storage photon generator 170 may generate and emitstorage photons having any wavelength, for example, between about 300 nmand about 10 μm, for example, 500 nm, 1550 nm, 2200 nm, or the like. Asa non-limiting example, the storage photon emitted by the storage photongenerator 170 may comprise a first entangled storage photon that isentangled with a second entangled storage photon simultaneously emittedby the storage photon generator 170. In operation, the first entangledstorage photon may traverse the doped polycrystalline ceramic opticaldevice 120 and the second entangled storage photon may travel along apathway separate from the doped polycrystalline ceramic optical device120 while remaining entangled with the first entangled storage photon.

Referring still to FIG. 1, the storage photon generator 170 may beoptically coupled to the doped polycrystalline ceramic optical device120 using a storage photon transmission fiber 172 or other waveguidedevice, which may extend between the storage photon generator 170 andthe first or second end 126, 128 of the doped polycrystalline ceramicoptical device 120. Further, the storage photon generator 170 may beoptically coupled to the first or second end 126, 128 of the dopedpolycrystalline ceramic optical device 120 by aligning the storagephoton generator 170 with the first end 126 or the second end 128, forexample, using one or more alignment mechanisms 142 structurallyconfigured to optically align the storage photon generator 170 with thedoped polycrystalline ceramic optical device 120. The one or morealignment mechanisms 142 may comprise an alignment stage, an opticalswitch, or both. Further, the storage photon generator 170 and/or thedoped polycrystalline ceramic optical device 120 may be coupled toindividual alignment mechanisms 142.

The one or more pump lasers 180 are optically coupled to the dopedpolycrystalline ceramic optical device 120 and are each structurallyconfigured to generate and emit pump pulses. The one or more pump lasers180 may comprise any laser source, for example, a diode laser, anexternal cavity diode laser, a fiber laser, a dye laser, or the like.Further, the one or more pump lasers 180 may be structurally configuredto emit pump pulses having any wavelength, for example, between about500 nm and about 2200 nm. Moreover, the wavelength of the pump pulsesgenerated and emitted by the one or more pump lasers 180 may be largerthan the wavelength of the storage photons generated and emitted by thestorage photon generator 170.

Further, as depicted in FIG. 1, the one or more pump lasers 180 maycomprise a first pump laser 180 a and a second pump laser 180 b. Forexample, the first pump laser 180 a may be optically coupled to thefirst end 126 of the doped polycrystalline ceramic optical device 120and the second pump laser 180 b may be optically coupled to the secondend 128 of the doped polycrystalline ceramic optical device 120. Asdepicted in FIG. 1, the first pump laser 180 a may be optically coupledto the same end of the doped polycrystalline ceramic optical device 120as the storage photon generator 170 (e.g., the first end 126) and thesecond pump laser 180 b may be optically coupled to a different end ofthe doped polycrystalline ceramic optical device 120 as the storagephoton generator 170 (e.g., the second end 128). Optically coupling thefirst and second pump lasers 180 a, 180 b to different ends of the dopedpolycrystalline ceramic optical device 120 may decrease opticalscattering within the doped polycrystalline ceramic optical device 120of the storage photon during operation of the quantum memory system 100.

As depicted in FIG. 1, each pump laser 180 may be optically coupled tothe doped polycrystalline ceramic optical device 120 using a pump pulsetransmission fiber 182 or other waveguide device, which may extendbetween each pump laser 180 and the doped polycrystalline ceramicoptical device 120. Further, each pump laser 180 may be opticallycoupled to the doped polycrystalline ceramic optical device 120 usingone or more alignment mechanisms 142 structurally configured tooptically align each pump laser 180 with the doped polycrystallineceramic optical device 120. The one or more alignment mechanisms 142 maycomprise an alignment stage, an optical switch, or both. Further, theone or more pump lasers 180 and/or the doped polycrystalline ceramicoptical device 120 may be coupled to individual alignment mechanisms142.

Referring again to FIG. 1, the quantum memory system 100 may furthercomprise a wavelength division multiplexer (WDM) 160 optically coupledto the doped polycrystalline ceramic optical device 120. In particular,the WDM 160 is optically coupled to the end of the doped polycrystallineceramic optical device 120 where the storage photon exits the dopedpolycrystalline ceramic optical device 120. For example, as depicted inFIG. 1, the WDM 160 may be optically coupled to the first end 126 of thedoped polycrystalline ceramic optical device 120. Further, the WDM 160may be optically coupled to both a storage photon pathway 162 and a pumppulse pathway 164, for example, the WDM 160 may be positioned between anend (e.g., the first end 126) of the doped polycrystalline ceramicoptical device 120 and both the storage photon pathway 162 and the pumppulse pathway 164. The WDM 160 is configured to direct the storagephotons into the storage photon pathway 162 and direct the pump pulsesinto the pump pulse pathway 164. For example, the WDM 160 may direct awavelength range of photons encompassing the wavelengths of the storagephotons into the storage photon pathway 162 and may direct a wavelengthrange of photons encompassing the wavelengths of the pump pulses intothe pump pulse pathway 164. Further, the storage photon pathway 162 andthe pump pulse pathway 164 may comprise optical fibers.

The storage photon pathway 162 may extend between the WDM 160 and astorage photon receiver 166. As one non-limiting example, the storagephoton receiver 166 may comprise an optical fiber link of one or morephoton entanglement chains of the quantum key generation systemdescribed in U.S. patent application Ser. No. 14/680,522. As anothernon-limiting example, the storage photon receiver 166 may compriserepeater entanglement optics 210 of the quantum repeater system 201 ofFIG. 4. Further, the pump pulse pathway 164 may extend between the WDM160 and a pump pulse receiver 168. In operation, the first and secondpump pulses may terminate at the pump pulse receiver 168, for example,the pump pulse receiver 168 may comprise a fiber end in embodiments inwhich the pump pulse pathway 164 comprises an optical fiber.

Referring still to FIG. 1, the quantum memory system 100 may furthercomprise an optical circulator 150 optically coupled the dopedpolycrystalline ceramic optical device 120, for example, to the firstend 126 of the doped polycrystalline ceramic optical device 120. Theoptical circulator 150 comprises three or more optical ports, forexample, a first optical port 152, a second optical port 154, and athird optical port 156. Further, the optical circulator 150 ispositioned between the storage photon generator 170 and the dopedpolycrystalline ceramic optical device 120, for example, the first end126 of the doped polycrystalline ceramic optical device 120 such that afirst optical port 152 of the optical circulator 150 is opticallycoupled to the storage photon generator 170 and the second port isoptically coupled to the first end 126 of the doped polycrystallineceramic optical device 120.

The optical circulator 150 may also be positioned between at least oneof the pump lasers 180 (e.g., the first pump laser 180 a) and the firstend 126 of the doped polycrystalline ceramic optical device 120 suchthat the first optical port 152 of the optical circulator 150 isoptically coupled to at least one of the one or more pump lasers 180 andthe second optical port 154 is optically coupled to the first end 126 ofthe doped polycrystalline ceramic optical device 120. For example, asdepicted in FIG. 1, the storage photon generator 170 and the first pumplaser 180 a are each optically coupled to the first optical port 152 ofthe optical circulator 150 such that storage photons output by thestorage photon generator 170 and the first pump pulse output by thefirst pump laser 180 a enter the first optical port 152 of the opticalcirculator 150 and exit the second optical port 154 towards the firstend 126 of the doped polycrystalline ceramic optical device 120.

The optical circulator 150 may also be positioned between the WDM 160and the doped polycrystalline ceramic optical device 120, for example,the first end 126 of the doped polycrystalline ceramic optical device120. Further, the third optical port 156 of the optical circulator 150is optically coupled to the WDM 160. For example, the WDM 160 ispositioned adjacent and optically coupled to the third optical port 156of the optical circulator 150 such that the WDM 160 receives the storagephoton after the storage photon exits the first end 126 of the dopedpolycrystalline ceramic optical device 120 and may receive one or bothof the pump pulses output by the first and second pump lasers 180 a, 180b.

As depicted in FIG. 1, the quantum memory system 100 may furthercomprise a cooling system 190 thermally coupled to the dopedpolycrystalline ceramic optical device 120. As a non-limiting example,the cooling system 190 may comprise a cooling chamber and the dopedpolycrystalline ceramic optical device 120 may be positioned within thecooling chamber. As another non-limiting example, the cooling system 190may comprise a laser cooling system and the doped polycrystallineceramic optical device 120 may be optically coupled to the laser coolingsystem. It should be understood that any cooling system 190 structurallyconfigured to cool the doped polycrystalline ceramic optical device 120is contemplated.

Referring still to FIG. 1, the magnetic field generation unit 140 maycomprise any magnetic device structurally and compositionally configuredto generate a magnetic field, for example, a static magnetic field. Asnon-limiting examples, the magnetic field generation unit 140 maycomprise an electromagnet, a ferromagnet, an alcnico magnet, a samariumcobalt (SmCo) magnet, a neodymium iron boron (NdFeB) magnet, orcombinations thereof. Further, the magnetic field generation unit 140 ispositioned within the quantum memory system 100 such that, when themagnetic field generation unit 140 generates a magnetic field, the dopedpolycrystalline ceramic optical device 120 is positioned within themagnetic field of the magnetic field generation unit 140. For example,the magnetic field generation unit 140 may be adjacent the dopedpolycrystalline ceramic optical device 120. As a non-limiting example,the magnetic field generation unit 140 may be structurally andcompositionally configured to generate a magnetic field comprising amagnetic flux density of between about 0.2 tesla and about 5 tesla, suchas about 0.4 tesla, 0.5 tesla, 0.6 tesla, 0.65 tesla, 0.7 tesla, 0.8tesla, 1 tesla, 2 tesla, 2.5 tesla, 3 tesla, 4 tesla, or the like.

As schematically depicted in FIG. 2, when the doped polycrystallineceramic optical device 120 is positioned within the magnetic field ofthe magnetic field generation unit 140 and the one or more pump lasers180 have irradiated the doped polycrystalline ceramic optical device 120to generate the shaped spectral structure within the rare-earth elementdopant 130, a ground state of the superposition of the shaped spectralstructure of the rare-earth element dopant 130 is split such that eachsuperposition of the shaped spectral structure of the rare-earth elementdopant 130 comprises a first split ground state G₁, a second splitground state G₂ and an excited energy state E₁. By splitting the groundstate of the superposition of the shaped spectral structure of therare-earth element dopant 130, the superposition of the shaped spectralstructure may be transferred into the second ground state G₂ to storethe storage photon within the doped polycrystalline ceramic opticaldevice 120, as described below.

In operation, the doped polycrystalline ceramic optical device 120 dopedwith the rare-earth element dopant 130 is structurally andcompositionally configured to absorb and store a storage photon emittedby the storage photon generator 170. For example, the shaped spectralstructure may be generated in the doped polycrystalline ceramic opticaldevice 120, for example, in the rare-earth element dopant 130, using oneor more pump pulses output by the pump laser 180. For example, theshaped spectral structure may comprise an atomic frequency comb (AFC),controlled reversible inhomogeneous broadening (CRIB), or any known oryet-to-be developed shaped spectral structure, for example, shapedspectral structures formed by using spectral hole burning. Exampleshaped spectral structures are described in Hastings-Simon et al.,“Controlled Stark shifts in Er³⁺-doped crystalline and amorphouswaveguides for quantum state storage,” Optics Communications, 266, pgs.716-719 (2006), Afzelius et al, “Multimode quantum memory based atomicfrequency combs,” Physical Review A 79, 052326 (2009), and Nilsson etal., “Solid state quantum memory using complete absorption andre-emission of photons by tailored and externally controlledinhomogeneous absorption profiles,” Optics Communications, 247, pgs.393-403 (2005).

Next, when the storage photon is traversing the doped polycrystallineceramic optical device 120, the storage photon may transfer thesuperposition of the shaped spectral structure of the rare-earth elementdopant 130 from the first split ground state G₁ to the excited energystate E₁, as schematically shown in FIG. 2, to absorb the storagephoton. Next, upon receipt of a first pump pulse output by the firstpump laser 180 a, the first pump pulse may transfer the superposition ofthe shaped spectral structure of the rare-earth element dopant 130 fromthe excited energy state E₁ into the second split ground state G₂, tostore the storage photon. Moreover, the output from the pump laser maycomprise a π-pulse.

Further, the doped polycrystalline ceramic optical device 120 doped withthe rare-earth element dopant 130 is structurally and compositionallyconfigured to release, on demand, the storage photon stored within thedoped polycrystalline ceramic optical device 120. For example, uponreceipt of a second pump pulse output by the second pump laser 180 b,the superposition of the shaped spectral structure of the rare-earthelement dopant 130 is transferred from the second split ground state G₂back to the excited energy state E₁. Once in the excited energy stateE₁, the superposition of the shaped spectral structure of the rare-earthelement dopant 130 will automatically release the storage photon after adelay period, such that the storage photon exits the dopedpolycrystalline ceramic optical device 120, for example, the first end126 of the doped polycrystalline ceramic optical device 120. Forexample, once in the excited energy state E₁, the shaped spectralstructure of the rare-earth element dopant 130 will rephase, and afterthe delay period, the storage photon will exit the doped polycrystallineceramic optical device 120. Moreover, the storage photon may exit thefirst end 126 of the doped polycrystalline ceramic optical device 120when the second pump laser 180 b emits the second pump pulse into to thesecond end 128 of the doped polycrystalline ceramic optical device 120and the storage photon may exit the second end 128 of the dopedpolycrystalline ceramic optical device 120 when the second pump laser180 b emits the second pump pulse into the first end 126 of the dopedpolycrystalline ceramic optical device 120.

The delay period comprises a consistent, repeatable time period, thus,upon repeated operation, individual storage photons are released afterthe same delay period. Further, different doped polycrystalline ceramicoptical devices 120 may comprise the same or different delay periods. Asa non-limiting example, doped polycrystalline ceramic optical devices120 comprising the same polycrystalline ceramic and dopant compositionmay comprise equal delay periods. Thus, a pair of the dopedpolycrystalline ceramic optical devices 120 having equivalent delayperiods may be arranged as the quantum repeater system 201 of theoptical system 200 of FIG. 4 and will each release storage photonssimultaneously if they each receive the second pump pulsesimultaneously, to facilitate quantum entanglement of storage photonsusing the repeater entanglement optics 210 of FIG. 4, as describedbelow. Further, the delay period of the individual doped polycrystallineceramic optical device 120 may be determined by performing a photon echomeasurement on the individual the doped polycrystalline ceramic opticaldevice 120.

Referring again to FIG. 1, the doped polycrystalline ceramic opticaldevice 120 may comprise a low phonon energy (e.g., Debye energy), whichmay limit unintended electron dephasing. For example, the dopedpolycrystalline ceramic optical device 120 may comprise a phonon energyof between about 100 cm⁻¹ and about 800 cm⁻¹, for example, 200 cm⁻¹, 300cm⁻¹, 400 cm⁻¹, 500 cm⁻¹, 600 cm⁻¹, 700 cm⁻¹, or the like. Electrondephasing refers to phonon assisted coupling from a trapped electronorbital to a degenerate or nearly degenerate orbital. Unintendedelectron dephasing refers to energy state transfer (e.g. phonon assistedcoupling) into the first ground state G₁ by the superposition of theshaped spectral structure of the rare-earth element dopant 130, thatcauses unintentional release of the storage photon before the desiredrelease of the storage photon. For example, unintended electrondephasing refers to electron (e.g., superposition) dephasing that occursbefore receipt of the first pump pulse or the second pump pulse by thedoped polycrystalline ceramic optical device 120. Further, loweringunintended electron dephasing may facilitate longer photon storagelifetimes and greater photon storage efficiency.

By lowering the phonon energy of the doped polycrystalline ceramicoptical device 120, the photon storage lifetime and the photon storageefficiency of the doped polycrystalline ceramic optical device 120 maybe increased. Photon storage lifetime refers to the maximum amount oftime a storage photon may remain stored within the doped polycrystallineceramic optical device 120 before unintended electron (e.g.,superposition) dephasing causes the storage photon to be released.Further, photon storage efficiency refers to the percentage of storagephotons traversing the doped polycrystalline ceramic optical device 120that are absorbed and stored. Moreover, the doped polycrystallineceramic optical device 120 comprises low attenuation, increasing thephoton storage efficiency. Attenuation may be lowered by reducingscattering, for example, by optically coupling the first and second pumplasers 180 a, 180 b to opposite ends of the doped polycrystallineceramic optical device 120, as depicted in FIG. 1. Further, attenuationmay be lowered by reducing the number of voids in the dopedpolycrystalline ceramic optical device 120. In some embodiments, thedoped polycrystalline ceramic optical device 120 is voidless.

Further, uniformly distributing the rare-earth element dopant 130 withinthe crystal lattice 122 of the doped polycrystalline ceramic opticaldevice 120 may prevent clustering of the rare-earth element dopant 130at the grain boundaries between individual crystals of the dopedpolycrystalline ceramic optical device 120. The uniform distribution mayreduce spin-spin interactions, thereby reducing unintended electrondecay. Moreover, by cooling the doped polycrystalline ceramic opticaldevice 120, for example, using the cooling system 190, the phononpopulation of the doped polycrystalline ceramic optical device 120 maybe reduced, increasing the photon storage lifetime and the photonstorage efficiency of the doped polycrystalline ceramic optical device120.

The doped polycrystalline ceramic optical device 120 may also compriseelements with a nuclear magnetic moment of about 3 μN or less, forexample, about 1 μN or less. In operation, lower magnetic moments arecorrelated with longer photon storage lifetime because of smallermagnetic dipole-dipole interaction of the element having a low nuclearmagnetic moment to the rare-earth element dopant 130. As a non-limitingexample, elements such as Y, Sn, and Pb, which each comprise lowmagnetic moments, may also be present in the doped polycrystallineceramic optical device 120. Further, doped polycrystalline ceramicoptical devices 120 comprising materials having higher atomic weightsmay be desired because heavier elements may also comprise lower phononenergy.

The doped polycrystalline ceramic optical device 120 doped with therare-earth element dopant 130 may also comprise a narrow homogeneouslinewidth, which may increase the photon storage lifetime and photonstorage efficiencies of the doped polycrystalline ceramic optical device120 doped with the rare-earth element dopant 130. In particular, anarrower homogeneous linewidth is directly correlated with a longerphoton storage lifetime. As used herein, inhomogeneous linewidth refersto the full-width half maximum (FWHM) spectral linewidth of theabsorption peak (e.g., wavelength at which maximum absorption occurs) ofthe rare-earth element dopant 130 of the doped polycrystalline ceramicoptical device 120. The inhomogeneous linewidth the dopedpolycrystalline ceramic optical device 120 doped with the rare-earthelement dopant 130 may comprise between about 1 nm and about 25 nm,between about 5 nm and 15 nm, or the like, for example, 2 nm, 5 nm, 10nm, 15 nm, 20 nm, or the like. Moreover, the homogeneous linewidth ofthe doped polycrystalline ceramic optical device 120 doped with therare-earth element dopant 130 may comprise about 7.5 MHz or less, forexample, 7 MHz, 6 MHz, 5 MHz 4 MHz, 3 MHz, 2 MHz, 1 MHz, or the like.

As one non-limiting example, the absorption peak of the dopedpolycrystalline ceramic optical device 120 doped with the rare-earthelement dopant 130 comprising erbium may be between about 1510 nm andabout 1550 nm, for example, between about 1535 nm and about 1545 nm,such as 1540 nm. As another non-limiting example, the absorption peak ofthe doped polycrystalline ceramic optical device 120 doped with therare-earth element dopant 130 comprising thulium may be between about1600 nm and about 1700 nm, for example, between about 1625 nm and about1675 nm, such as 1660 nm. Further, in operation, the dopedpolycrystalline ceramic optical device 120 doped with the rare-earthelement dopant 130 is configured to absorb and store a storage photontraversing the doped polycrystalline ceramic optical device 120, asdescribed above, upon receipt of a first pump pulse output by the firstpump laser 180 a that comprises a wavelength within 15 nm of thewavelength of the absorption peak, for example, within 10 nm, within 5nm, or equal to the wavelength of the absorption peak. Further, thedoped polycrystalline ceramic optical device 120 doped with therare-earth element dopant 130 may release the storage photon, asdescribed above, upon receipt of a second pump pulse output by thesecond pump laser 180 b that comprises a wavelength within 15 nm of thewavelength of the absorption peak, for example, within 10 nm, within 5nm, or equal to the wavelength of the absorption peak.

The relationship between photon storage lifetime and homogeneouslinewidth may be mathematically described with the following equations:

${\rho_{1} = {{\frac{1}{c}\frac{3}{2\;\pi\;\rho\; v^{5}\hslash^{4}}{\left\langle {\psi_{i}^{el}{V_{1}}\psi_{j}^{el}} \right\rangle }^{2}\mspace{14mu}{and}\mspace{14mu}\rho_{2}} = {\frac{1}{c}\frac{3}{2\;\pi\;\rho\; v^{2}\hslash^{4}}{\left\langle {\psi_{i}^{el}{V_{2}}\psi_{i}^{el}} \right\rangle }^{2}}}},$where, V₁ is the first spatial derivative of the crystal field of thedoped polycrystalline ceramic optical device 120, V₂ is the secondspatial derivative of the crystal field of the doped polycrystallineceramic optical device 120, ρ₁ is the probability amplitude of thetransition due to the V₁, ρ₂ is the probability of the transition due toV₂, c is the speed of light, ρ is the density of the host material, forexample, the doped polycrystalline ceramic optical device 120, v is theaverage velocity of a sound wave in the crystal, ψ_(i) ^(el) is theground state of the electron (e.g., the electron of the rare-earthelement dopant 130), and ψ_(j) ^(el) is the excited state of theelectron (e.g., the electron of the rare-earth element dopant 130).Further, a phonon coupling coefficient β_(ij) may be mathematicallydescribed as β_(ij)=

³cω_(ij) ³ρ₁, where c is the speed of light, ω_(i) is the homogeneouslinewidth of the doped polycrystalline ceramic optical device 120, andρ₁ is the is the first order probability amplitude of the transition. Asshown above, smaller (e.g., narrower) homogeneous linewidths generatesmaller photon coupling coefficients. Further, a small phonon couplingcoefficient is correlated with low phonon energy and low phonon energyfacilitates longer photon storage lifetimes. Thus, the homogeneouslinewidth is inversely proportional to the photon storage lifetime andnarrower homogeneous linewidth facilitate longer photon storagelifetimes.

Combining the above equations, the homogeneous lifetime may also bemathematically described as

${w_{i}^{\hom}\left( {cm}^{- 1} \right)} = {{{\frac{2\;\hslash\;{c\left( {kT}_{D} \right)}^{7}}{\pi}\left\lbrack {{\sum\limits_{i \neq j}\;\frac{p_{1}}{E_{i} - E_{j}}} + p_{2}} \right\rbrack}^{2}\left( \frac{T}{T_{D}} \right)^{7}{\int_{0}^{T_{D}/T}{\frac{x^{6}e^{x}}{\left( {e^{x} - 1} \right)^{2}}{dx}}}} + {p_{1}\left\{ {{\sum\limits_{j < i}\;{\Delta\;{E_{ij}^{3}\left( \frac{e^{\Delta\;{E_{ij}/{kT}}}}{e^{\Delta\;{E_{ij}/{kT}}} - 1} \right)}}} + {\sum\limits_{j < i}\;{\Delta\;{E_{ji}^{3}\left( \frac{1}{e^{\Delta\;{E_{ji}/{kT}}} - 1} \right)}}}} \right.}}$where c is the speed of light, k is the Boltzmann constant, T is thetemperature (e.g., the temperature of the doped polycrystalline ceramicoptical device 120), T_(D) is the Debye temperature, ρ₁ is the firstorder probability amplitude of the transition, ρ₂ is the second orderprobability amplitude of the transition, and E is the energy level.

In some embodiments, the rare-earth element dopant 130 may comprise anon-Kramers rare-earth ion, such as Pr³⁺, Tm³⁺, or the like. Dopedpolycrystalline ceramic optical device 120 doped with non-Kramersrare-earth ions may comprise a narrower homogeneous linewidth than dopedpolycrystalline ceramic optical devices 120 doped with Kramersrare-earth ions, for example, due to the lack of Kramers degeneracy ofnon-Kramers rare-earth ions. This may increase the photon storagelifetime of the doped polycrystalline ceramic optical device 120 andreduce unintended electron decay. Moreover, when the rare-earth elementdopant 130 comprises thulium, the electrons of the rare-earth elementdopant 130 comprising thulium may split into first and second groundstates G₁ and G₂ (FIG. 2) when positioned within a weaker magnetic fieldthan a rare-earth element dopant 130 comprising erbium.

Referring again to FIGS. 1 and 2, a method of storing and releasing astorage photon using the quantum memory system 100 is contemplated.While the method is described below in a particular order, it should beunderstood that other orders are contemplated. Referring now to FIG. 1,the method may first comprise generating a magnetic field using themagnetic field generation unit 140. As stated above, generating amagnetic field using the magnetic field generation unit 140 causes theground state of electrons of the rare-earth element dopant 130 doped issplit into the first ground state G₁ and the second ground state G₂, asdepicted in FIG. 2.

The method further generating a shaped spectral structure within therare-earth element dopant 130 of the doped polycrystalline ceramicoptical device 120 by irradiating the doped polycrystalline ceramicoptical device 120 with a plurality of pump pulses output by the one ormore pump lasers 180. Next, the method comprises emitting a storagephoton from the storage photon generator 170 optically coupled to thedoped polycrystalline ceramic optical device 120 and upon receipt of thestorage photon by the doped polycrystalline ceramic optical device 120,the rare-earth element dopant 130 doped within the doped polycrystallineceramic optical device 120 absorbs the storage photon by transferring asuperposition of the shaped spectral structure of the rare-earth elementdopant 130 from the first split ground state G₁ to the excited energystate E₁. For example, the storage photon may comprise a wavelength ofbetween about 300 nm and about 10 μm, for example, 500 nm, 1550 nm, 2200nm. Next, the method further comprises emitting a first pump pulse fromthe first pump laser 180 a optically coupled to the dopedpolycrystalline ceramic optical device 120 such that the first pumppulse transfers the superposition of the shaped spectral structure ofthe rare-earth element dopant 130 from the excited energy state to asecond split ground state G₂, upon receipt of the first pump pulse bythe doped polycrystalline ceramic optical device 120, to store thestorage photon within the doped polycrystalline ceramic optical device120.

Referring still to FIGS. 1 and 2, the method further comprises emittinga second pump pulse from the second pump laser 180 b such that thesecond pump pulse transfers the superposition of the shaped spectralstructure of the rare-earth element dopant 130 from the second splitground state G₂ to the excited energy state E₁, upon receipt of thesecond pump pulse by the doped polycrystalline ceramic optical device120. Once back in the excited energy state E₁, the superposition of theshaped spectral structure of the rare-earth element dopant 130 willautomatically release the storage photon after a delay period, such thatthe storage photon exits the doped polycrystalline ceramic opticaldevice 120.

Further, in operation, the quantum memory system 100 and moreparticularly, the doped polycrystalline ceramic optical device 120 dopedwith a rare-earth element dopant 130 may absorb and store a storagephoton for a photon storage lifetime comprising between about 500 ns andabout 1 ms, for example, between about 1 μs and about 1 ms or betweenabout 10 μs and about 1 ms. Moreover, in operation, the quantum memorysystem 100 and, more particularly, the doped polycrystalline ceramicoptical device 120 doped with a rare-earth element dopant 130 may absorband store about 50% or more of a plurality of storage photons traversingthe doped polycrystalline ceramic optical device 120, for example, about70% or more of the plurality of storage photons traversing the dopedpolycrystalline ceramic optical device 120, about 90% or more of theplurality of storage photons traversing the doped polycrystallineceramic optical device 120, or the like.

Referring now to FIGS. 3A and 3B, a method of manufacturing the dopedpolycrystalline ceramic optical device 120 of FIG. 1 is contemplated.While the method is described below in a particular order, it should beunderstood that other orders are contemplated. As depicted in FIG. 3A,the method first comprises mixing a plurality of transition metalcomplexes 112, a plurality of rare-earth metal complexes 114, an organicprecursor 116, and water, such as, deionized water, to form a precursormixture 111. The plurality of transition metal complexes 112 maycomprise metal complexes, such as metal salts, which include atransition metal, for example, zirconium, yttrium, or combinationsthereof. Further, the transition metals of plurality of transition metalcomplexes 112 may include cubic crystals of a dielectric material andmay each comprise a cross-sectional dimension (e.g., diameter) ofbetween about 25 nm and about 250 nm, for example, 50 nm, 75 nm, 100 nm,125 nm, 150 nm, 200 nm, or the like. As one example, the plurality oftransition metal complexes 112 may comprise YCl₃.6H₂O.

Further, the plurality of rare-earth metal complexes 114 may comprisemetal complexes, such as metal salts, that include any of the rare-earthelements described above. As one example, the rare-earth metal complexes114 may comprise ErCl₃.6H₂O. As stated above, by using rare-earth metalcomplexes 114 to form the plurality of rare-earth doped nanoparticles110 the rare-earth element dopant 130 positioned within resultant dopedpolycrystalline ceramic optical device 120 may be more uniformlydistributed within the crystal lattice 122 of the doped polycrystallineceramic optical device 120, improving performance of the dopedpolycrystalline ceramic optical device 120. Moreover, the organicprecursor 116 may comprise urea, ammonium hydroxide, or the like.

As one example, the precursor mixture 111 may include between about 40 gand about 80 g of the transition metal complexes 112, for example, about50 g, 60 g, 65 g, 65.53 g, 70 g, or the like. The precursor mixture 111may also include between about 0.01 g and about 0.5 g of the rare-earthmetal complexes 114, for example, about 0.05 g, 0.1 g, 0.15 g, 0.2 g,0.25 g, 0.35 g, or the like. Further, the precursor mixture 111 mayinclude between about 350 g and about 450 g of the organic precursor116, for example, about 375 g, 388.8 g, 400 g, 425 g, or the like.Moreover, the precursor mixture 111 may include between about 2 L andabout 6 L of deionized water, for example, about 3 L, 4 L, 4.32 L, 5 L,or the like.

Referring still to FIGS. 3A and 3B, the method further comprises heatingthe plurality of transition metal complexes 112, the plurality ofrare-earth metal complexes 114, the organic precursor 116, and thedeionized water (e.g., the precursor mixture 111) to a heatingtemperature for a heating period to induce thermal decomposition of theorganic precursor 116 and generate a chemical reaction between thetransition metal complexes 112, the rare-earth metal complexes 114, andthe organic precursor 116 to produce a plurality of rare-earth dopednanoparticles 110, as depicted in FIG. 3B. For example, the heatingtemperature may be between about 70° C. and about 100° C., such as about80° C., 90° C., 95° C., or the like, and the heating period may bebetween about 0.5 hours and about 3 hours, such as, 1 hour, 2 hours, orthe like.

In operation, the thermal decomposition of the organic precursor 116,such as urea, may produce OH⁻ and CO₃ ²⁻, which react with thetransition metals of the plurality of transition metal complexes 112 andthe rare-earth metals of the plurality of rare-earth metal complexes 114to produce the plurality of rare-earth doped nanoparticles 110, forexample, Y_(1-x)Er_(x)(OH)CO₃.H₂O nanoparticles. Further, theY_(1-x)Er_(x)(OH)CO₃.H₂O nanoparticles may be filtered and collectedthen annealed at an annealing temperature of between about 500° C. andabout 900° C., such as about 600° C., 700° C., 800° C., or the like, toconvert the Y_(1-x)Er_(x)(OH)CO₃.H₂O rare-earth doped nanoparticles 110into (Y_(1-x)Er_(x))₂O₃ rare-earth doped nanoparticles 110. Onceannealed, the rare-earth doped nanoparticles 110 may comprise acrystalline structure. Moreover, the chemical yield of the rare-earthdoped nanoparticles 110 may be between about 85% and about 98%, forexample 88%, 90%, 92%, 95%, or the like.

The diameter of the plurality of rare-earth doped nanoparticles 110 maybe altered by varying the concentration of the plurality of transitionmetal complexes 112 in the precursor mixture 111. As one example, whenthe concentration of plurality of transition metal complexes 112 in theprecursor mixture 111 is about 0.0125 M, the diameter of the resultingrare-earth doped nanoparticles 110 may be about 100 nm. As anotherexample, when the concentration of plurality of transition metalcomplexes 112 in the precursor mixture 111 is about 0.05 M, the diameterof the resulting rare-earth doped nanoparticles 110 may be about 150 nm.Further, it may be desirable that the plurality of transition metalcomplexes 112 in the precursor mixture 111 is less than 0.05 M, becausethe resulting rare-earth doped nanoparticles 110 may be non-uniform andagglomerated if the concentration of transition metal complexes 112 inthe precursor mixture 111 is greater than 0.05 M.

Further, the amount of rare-earth element dopant in the plurality ofrare-earth doped nanoparticles 110 may be altered by changing the ratioof transition metal complexes 112 and rare-earth metal complexes 114 inthe precursor mixture 111. As one example, when the ratio of thetransition metal complexes 112 and the rare-earth metal complexes 114 isabout 137 parts of the plurality of transition metal complexes 112 toabout 1 part of the plurality of rare-earth metal complexes 114, theresulting rare-earth doped nanoparticles 110 may comprise about 0.97%rare-earth element dopant. As another example, when the ratio of theplurality of transition metal complexes 112 and the plurality ofrare-earth metal complexes 114 is about 548 parts of the plurality oftransition metal complexes 112 to about 1 part of the plurality ofrare-earth metal complexes 114, the resulting rare-earth dopednanoparticles 110 may comprise about 0.25% rare-earth element dopant.

The method may further include milling the plurality of rare-earth dopednanoparticles 110 using a milling media, for example, a yttriastabilized grinding media, such as YTZ® grinding media manufactured byTosoh Corporation, Tokyo Japan. The milling media may comprise adiameter between about 1 mm and 3 mm, for example, 1.5 mm, 2 mm, 2.5 mm,or the like. Further, additional materials may be added before or duringthe milling process, for example, a mixture of ethanol solvents,1-butanol, propylene glycol, organophosphate, such as Phosphalon™PS-236, and deionized water. In operation, the rare-earth dopednanoparticles 110 may be milled for between about 75 hours and about 100hours, for example, about 80 hours, 85 hours, 90 hours, 95 hours, or thelike. Moreover, the rare-earth doped nanoparticles 110 may be milledusing a VIBRA-MILL® milling system.

As one example, about 25 g of the rare-earth doped nanoparticles 110 maybe milled using between about 100 g and about 150 g of milling media,for example, 110 g, 120 g, 130 g, 140 g, or the like. Further, theadditional materials added before or during the milling process mayinclude about 15 g and about 20 g of ethanol solvents, for example,about 16 g, 17 g, 18 g, 18.3 g, 19 g, or the like, between about 2 g andabout 6 g of 1-butanol, for example, about 3 g, 4 g, 4.4 g, 5 g, or thelike, between about 0.5 g and about 1.5 g of propylene glycol, such asabout 1.0 g, between about 0.25 g and about 0.5 g of an organophosphate,such as Phosphalon™ PS-236, for example, about 0.3 g. 0.35 g, 0.38 g,0.4 g, 0.45 g, or the like, and between about 0.5 g and about 2.5 g ofdeionized water, for example, about 1 g, 1.3 g, 1.5 g, 2 g, or the like.

In operation, the milling process disperses the plurality of rare-earthdoped nanoparticles 110 into a slurry, which may be separated from themilling media during a filtration process, for example, using a screen.Next, one or more binders, such as Butvar® polyvinyl butyral (PVB-B98)and one or more plasticizers, such as dibutyl phthalate, may be added tothe slurry having the rare-earth doped nanoparticles 110, which may thenbe mixed, for example, using a Mazerustar™ planetary mixer (such asmodel KK-400W). Next, the slurry having the plurality of rare-earthdoped nanoparticles 110 may be rolled, for example, using rollersoperating at about 25 RPM for about 18-24 hours to remove air within theslurry having the rare-earth doped nanoparticles 110. By removing air,the resulting doped polycrystalline ceramic optical device 120 (e.g.,formed using the sintering process described below) may be voidless. Inoperation, a longer milling process, for example, a milling process ofabout 90 hours or longer, may be desired to reduce the voids andincrease the transparency of the resultant doped polycrystalline ceramicoptical device 120.

In some embodiments, the slurry having the rare-earth dopednanoparticles 110 may be cast into a film using a casting process suchas a tape casting process, for example, using a TAM Ceramics®hydraulically driven tape caster. After casting, the film having therare-earth doped nanoparticles 110 may be dried, for example, bycovering the film with a covering material such that an air gap islocated between the film and the covering material for a drying period,for example, between about 18 hours and about 24 hours, e.g., 20 hours,22 hours, or the like. Next, the film having the rare-earth dopednanoparticles 110 may be dried in a drying oven at about 50° C. forabout 20-25 mins, which may remove organics present in the film havingthe rare-earth doped nanoparticles 110. Further, the film having therare-earth doped nanoparticles 110 may have a thickness of about 100 μmor less, for example, about 75 μm, 50 μm, 25 μm, 20 μm, 15 μm, 10 μm, orthe like.

The method of manufacturing the doped polycrystalline ceramic opticaldevice 120 may further comprise sintering the plurality of rare-earthdoped nanoparticles 110, for example, sintering the film having therare-earth doped nanoparticles 110 to form the doped polycrystallineceramic optical device 120 having a rare-earth element dopant 130,described above. Before sintering, the film having the rare-earth dopednanoparticles 110 may be placed on a setter, such as an alumina setter.Once placed on the setter, the film having the rare-earth dopednanoparticles 110 may be sintered using a sintering furnace, such as aCM™ Furnace.

As one example, during the sintering process, the film having therare-earth doped nanoparticles 110 may be sintered using the followingsintering schedule. First, the film having the rare-earth dopednanoparticles 110 may be heated from room temperature to 200° C. for aheating period of about 1 hour then the film may be heated from about200° C. to about 500° C. for a heating period of about 2 hours thenheated from 500° C. to about 1550° C. for a heating period of about 5hours. Next, the film having the rare-earth doped nanoparticles 110 maybe maintained at a temperature of about 1550° C., for example, atemperature at least about 1500° C. or greater, for a dwelling period ofabout 2 hours, then cooled from 1550° C. to about room temperature overa cooling period of about 3 hours. In operation, a higher maximumtemperature during the sintering process, for example, a maximumtemperature of about 1550° C. or more may be desired to reduce the voidsand increase the transparency of the resultant doped polycrystallineceramic optical device 120.

In other embodiments, the plurality of rare-earth doped nanoparticles110 may be pressed into a pellet before undergoing the sinteringprocess. For example, the plurality of rare-earth doped nanoparticles110 may be pressed into a pellet instead of being formed into a slurrythen cast into a film. In operation, the plurality of rare-earth dopednanoparticles 110 may be pressed, for example, uni-axially pressed,iso-statically pressed, or both into a pellet having the rare-earthdoped nanoparticles 110. The pellet having the rare-earth dopednanoparticles 110 may be uni-axially pressed in a ¾ inch steel die atabout 8 K pounds force and/or iso-statically pressed at about 25 Kpsiusing an iso-pressing sheath, for example, a latex iso-pressing sheath.After pressing, the pellets may be sintered. During the sinteringprocess, the pellets may be heated from room temperature to a maximumtemperature over a period of about 12 hours and may be maintained at themaximum temperature for about 2 hours. Further, the maximum temperatureof between about 1300° C. and 1800° C., for example, about 1400° C.,1450° C., 1500° C., 1515° C. 1550° C., 1600° C., 1615° C., 1650° C.,1700° C., or the like. Next, the pellet may be cooled back to roomtemperature for a cooling period of about 12 hours. Further, it shouldbe understood that sintering the pellet having the rare-earth dopednanoparticles 110 forms the doped polycrystalline ceramic optical device120 having a rare-earth element dopant 130, described above.

After sintering, the pellet may also be hot iso-statically pressed at atemperature of between about 1400° C. and about 1800° C., for example,about 1515° C., 1625° C. 1650° C., or the like. Further, the pellethaving the rare-earth doped nanoparticles 110 may be placed under highpressure while heated, for example, for about the 4 hours at about 29Kpsi. Moreover, during the hot iso-static pressing process, the pellethaving the rare-earth doped nanoparticles 110 may be placed in argon oranother noble gas. In some embodiments, the maximum temperature reachedduring the sintering process may be greater than the maximum temperaturereached during the hot iso-static pressing process. After hotiso-statically pressing the pellet having the rare-earth dopednanoparticles 110, the pellet may be polished, for example, to a 0.5 μmdiamond finish. After polishing, the pellet may be oxidized at 1100° C.in air for 2 hours then annealed. Annealing may remove any carbon thatdiffused into the pellet during hot iso-static pressing process. Suchcarbon contamination can be removed by annealing the pellet in air atabout 1200° C. for about 12 hours. The annealing process may then berepeated, for example, for about 4 hours. It should be understood thatsintering the pellet having the rare-earth doped nanoparticles 110 formsthe doped polycrystalline ceramic optical device 120 having a rare-earthelement dopant 130, described above.

Referring now to FIGS. 3C-3E, another method of manufacturing the dopedpolycrystalline ceramic optical device 120 of FIG. 1 is contemplated. Asdepicted in FIG. 3A, the method first comprises mixing the plurality oftransition metal complexes 112, the plurality of rare-earth metalcomplexes 114, and deionized water to form a metal salt solution 115. Asone example, the metal salt solution 115 may include between about 40 gand about 80 g of the transition metal complexes 112, for example, about50 g, 60 g, 65 g, 65.53 g, 70 g, or the like. The metal salt solution115 may also include between about 0.01 g and about 0.5 g of therare-earth metal complexes 114, for example, about 0.05 g, 0.1 g, 0.15g, 0.2 g, 0.25 g, 0.35 g, or the like. Moreover, the metal salt solution115 may include between about 2 L and about 6 L of deionized water, forexample, about 3 L, 4 L, 4.32 L, 5 L, or the like. In one example, themetal salt solution 115 may comprise about 0.2-0.25 moles of metal salts(e.g., the plurality of transition metal complexes 112 and the pluralityof rare-earth metal complexes 114) in about 4 L of deionized water).

Referring still to FIGS. 3C-3E, the method further comprises heating themetal salt solution 115 to form a heated metal salt solution 115′. Forexample, the metal salt solution 115 may be heated to a temperature offrom about 70° C. to about 100° C., such as about 80° C., 90° C., 100°C., or the like. As one example, the heated metal salt solution 115′ maybe heated to a boil. Next, as depicted in FIG. 3D, the organic precursor116 may be mixed with the heated metal salt solution 115′, inducingformation of the rare-earth doped nanoparticles 110. In someembodiments, the temperature of the organic precursor 116 may be lessthan the temperature of the heated metal salt solution 115′ when mixedwith the heated metal salt solution 115′, and in other embodiments, theorganic precursor 116 may be the same temperature or a greatertemperature than the heated metal salt solution 115′.

Further, preforming the heated metal salt solution 115′ then mixing theorganic precursor 116 with the heated metal salt solution 115′ mayinduce formation of rare-earth doped nanoparticles 110 that have asmaller diameter than rare-earth doped nanoparticles 110 formed usingthe precursor mixture 111 described above with respect to FIGS. 3A and3B. For example, the rare-earth doped nanoparticles 110 formed by mixingthe organic precursor 116 and the heated metal salt solution 115′ maycomprise 200 nm or less, such as 100 nm or less, 50 nm or less, 40 nm orless, 30 nm or less, or the like. While not intending to be limited bytheory, it is believed that mixing the organic precursor 116 and theheated metal salt solution 115′ produces more rare-earth doped nuclei,thereby forming smaller rare-earth doped nanoparticles 110.

In operation, the thermal decomposition of the organic precursor 116,such as urea, may produce OH⁻ and CO₃ ²⁻, which react with thetransition metals of the plurality of transition metal complexes 112 andthe rare-earth metals of the plurality of rare-earth metal complexes 114of the heated metal salt solution 115′ to produce the plurality ofrare-earth doped nanoparticles 110, for example,Y_(1-x)Er_(x)(OH)CO₃.H₂O nanoparticles. Further, theY_(1-x)Er_(x)(OH)CO₃.H₂O nanoparticles may be filtered and collectedthen annealed at an annealing temperature of between about 500° C. andabout 900° C., such as about 600° C., 700° C., 800° C., or the like, toconvert the Y_(1-x)Er_(x)(OH)CO₃.H₂O rare-earth doped nanoparticles 110into (Y_(1-x)Er_(x))₂O₃ rare-earth doped nanoparticles 110. Onceannealed, the rare-earth doped nanoparticles 110 may comprise acrystalline structure. Moreover, the chemical yield of the rare-earthdoped nanoparticles 110 may be between about 85% and about 98%, forexample 88%, 90%, 92%, 95%, or the like.

Further, in the method of FIGS. 3C-3E, the amount of rare-earth elementdopant in the plurality of rare-earth doped nanoparticles 110 may bealtered by changing the ratio of transition metal complexes 112 andrare-earth metal complexes 114 in the metal salt solution 115. Forexample, increasing the relative amount of rare-earth metal complexes114 in the metal salt solution 115 may increase the amount of rare-earthelement dopant in the resultant plurality of rare-earth dopednanoparticles 110. The method depicted in FIGS. 3C-3E may furtherinclude milling the plurality of rare-earth doped nanoparticles 110using a milling media to form a slurry, filtering the milling media fromthe slurry, and adding one or more binders to the slurry, as describedabove with respect to FIGS. 3A and 3B.

Referring still to FIGS. 3C-3E, the method of manufacturing the dopedpolycrystalline ceramic optical device 120 may next comprising sinteringthe plurality of rare-earth doped nanoparticles 110 using any of thesintering processes described above with respect to FIGS. 3A and 3B. Inone example process, the plurality of rare-earth doped nanoparticles 110may be pressed into a pellet of rare-earth doped nanoparticles 110, forexample, using a steel die at from about 6 Klbs of force to about 10Klbs of force, such as about 8 Klbs of force. Next, the pellet ofrare-earth doped nanoparticles 110 may be isostatically pressed at roomtemperature, for example, using a latex iso-pressing sheath, at fromabout 20 Kpsi to about 30 Kpsi, for example, 25 Kpsi. The pellet ofrare-earth doped nanoparticles 110 may then be sintered at a sinteringtemperature of 1300° C. or more, for a sintering period of from about1.5 hours to about 2.5 hours, for example, about 2 hours. Aftersintering, the pellet of rare-earth doped nanoparticles 110 may then behot isostatically pressed at a temperature of from about 1300° C. toabout 1600° C. (e.g., 1500° C.) for a hot isostatic pressing period offrom about 14 hours to about 18 hours (e.g., 16 hours), at a pressure ofabout 15 Kpsi to about 35 Kpsi (e.g., 29 Kpsi). The hot isostaticpressing step may occur in a graphite furnace in the presence of argon.During hot isostatically pressing, the pellet of rare-earth dopednanoparticles 110 may be positioned in Y₂O₃ powder (e.g., buried) toreduce carbon contaminations. In operation, the hot isostatic pressingmay densify (e.g., increase the density) of the pellet of rare-earthdoped nanoparticles 110. After formation, the doped polycrystallineceramic optical device may be polished to a surface finish of about 0.5μm Ra.

In one example manufacturing process, the pellet of rare-earth dopednanoparticles 110 may first be sintered at a sintering temperature ofabout 1550° C. then isostatically pressed at a temperature of about1515° C. In a second example manufacturing process, the pellet ofrare-earth doped nanoparticles 110 may first be sintered at a sinteringtemperature of about 1550° C. then isostatically pressed at atemperature of about 1515° C. In a third example manufacturing process,the pellet of rare-earth doped nanoparticles 110 may first be sinteredat a sintering temperature of about 1550° C. then isostatically pressedat a temperature of about 1515° C. In each of the three examplemanufacturing processes above, the sintering pressure may about 29 Kpsi,the sintering period may be about 2 hours, and the hot isostaticpressing period may be about 16 hours. Further, in each of the threeexample processes, the hot isostatic pressing temperature may be lessthan the sintering process, which minimizes crystal grain growth duringhot isostatic pressing.

Further, the resultant doped polycrystalline ceramic optical device 120formed using the methods of manufacture of FIGS. 3C-3E may be configuredto facilitate an axial optical transmission of a plurality of photonstraversing the doped polycrystalline ceramic optical device 120 eachcomprising a wavelength of from about 1000 nm to about 2000 nm, such asabout 1535 nm, 1550 nm, or the like, of from about 70% to about 82%, forexample 75%, 77%, 80%, 81%, 81.5%, 81.7%, or the like. Further, ascattering angle of the plurality of photons may be about 2.5°.Individual crystals of the doped polycrystalline ceramic optical device120 may comprise a grain size (e.g., largest dimension of each crystal)of from about 0.15 μm to about 2.5 μm, for example, about 0.2 μm, 0.4μm, 0.6 μm, 0.8 μm, 1 μm, 1.2 μm, 1.4 μm, 1.6 μm, 1.8 μm, 2 μm, 2.2 μm,2.4, μm, or the like. Further, an average grain area of the individualcrystals of the doped polycrystalline ceramic optical device 120 may befrom about 0.25 μm² to about 0.35 μm², for example, 0.26 μm², 0.27 μm²,0.28 μm², 0.29 μm², 0.3 μm², 0.31 μm², 0.32 μm², 0.33 μm², 0.34 μm², orthe like. Further, the grain size may be tuned by varying the sinteringtemperature during the sintering process. For example, higher sinteringtemperatures may form crystals comprising larger grain areas. As oneexample, when the pellet of rare-earth doped nanoparticles 110 issintered at a temperature of about 1550° C., the individual crystals ofthe doped polycrystalline ceramic optical device 120 may comprise agrain size of from about 0.7 μm to about 2.1 μm.

In operation, the sintering temperature used to form the dopedpolycrystalline ceramic optical device 120 is correlated with the sizeand density of scattering centers, such as residue pores, formed withinthe doped polycrystalline ceramic optical device 120. Lower sinteringtemperatures lower the size and density of the scattering centers, whichcause scattering induced attenuation when photons traverse the dopedpolycrystalline ceramic optical device 120. Thus, reducing the size anddensity of scattering centers may reduce the attenuation rate of photonstraversing the doped polycrystalline ceramic optical device 120. When aplurality of photons, such as storage photons, traverse the dopedpolycrystalline ceramic optical device 120, the scattering inducedattenuation of the plurality of photons may be defined by a transmittedscattering coefficient μ, where

${\mu = 10^{\frac{\log{({T_{t}/T_{a}})}}{L}}},$T_(t) is the total optical transmission of the plurality of photonthrough the doped polycrystalline ceramic optical device 120, T_(a) isaxial optical transmission of the plurality of photons traversing thedoped polycrystalline ceramic optical device 120, and L is the thicknessof the doped polycrystalline ceramic optical device 120. The axialoptical transmission T_(a) of the plurality of photons traversing thedoped polycrystalline ceramic optical device 120 is increased whenscattering centers are reduced and as such, forming the dopedpolycrystalline ceramic optical device 120 using lower sinteringtemperatures may reduce the scattering induced attenuation and theoverall attenuation rate of photons traversing the doped polycrystallineceramic optical device 120

Moreover, a doped polycrystalline ceramic optical device 120 formedusing smaller diameter rare-earth doped nanoparticles 110 may facilitatea lower attenuation rate than doped polycrystalline ceramic opticaldevices 120 formed using larger diameter rare-earth doped nanoparticles110. For example, the doped polycrystalline ceramic optical device 120formed using the methods of manufacture described with respect to FIGS.3C-3E may comprise an attenuation rate of 5 dB/mm or less, 4 dB/mm orless, 3 dB/mm or less, 2 dB/mm or less, 1 dB/mm or less, or the like.

Referring now to FIG. 4, an optical system 200 comprising a quantumrepeater system 201, one or more magnetic field generation units 240,and one or more pump lasers 280, is schematically depicted. The quantumrepeater system 201 includes first and second doped polycrystallineceramic optical devices 220 a, 220 b and repeater entanglement optics210. Further, the first and second doped polycrystalline ceramic opticaldevices 220 a, 220 b may each comprise the doped polycrystalline ceramicoptical device 120 described above with respect to the quantum memorysystem 100.

For example, the first and second doped polycrystalline ceramic opticaldevice 220 a, 220 b each comprise a first end 226 and a second end 228that may be opposite the first end 226. Further, the first and seconddoped polycrystalline ceramic optical devices 220 a, 220 b are dopedwith a rare-earth element dopant 230 that is uniformly distributedwithin a crystal lattice 222 a, 222 b of each of first and second dopedpolycrystalline ceramic optical device 220 a, 220 b. The rare-earthelement dopant 230 a, 230 b may comprise any of the rare-earth elementdopants 130 described above. Further, the first and second dopedpolycrystalline ceramic optical devices 220 a, 220 b may comprise dopedpolycrystalline ceramic optical waveguides, as described above.Moreover, the quantum memory system 100 may further comprise a coolingsystem 290 thermally coupled to each doped polycrystalline ceramicoptical device 220 a, 220 b. The cooling system 290 may comprise any ofthe cooling systems 190 described above.

The one or more magnetic field generation units 250 may comprise themagnetic field generation units 140 described above. Further, the firstand second doped polycrystalline ceramic optical devices 220 a, 220 bare positioned within a magnetic field of the one or more magnetic fieldgeneration units 250 when the one or more magnetic field generationunits 250 generate magnetic fields. Further, while a single magneticfield generation unit 250 is depicted in FIG. 3, it should be understoodthat any number of magnetic field generation units 250 are contemplated.For example, the first and second doped polycrystalline ceramic opticaldevice 220 a, 220 b may be positioned within the magnetic fields ofdifferent magnetic field generation units 250.

Referring still to FIG. 4, the optical system 200 further comprises oneor more storage photon generators 270 a, 270 b optically coupled to eachdoped polycrystalline ceramic optical devices 220 a, 220 b, for example,optically coupled to the first end 226 a, 226 b of each dopedpolycrystalline ceramic optical device 220 a, 220 b. For example, thefirst storage photon generator 270 a may be optically coupled to thefirst end 226 a of the first doped polycrystalline ceramic opticaldevice 220 a and the second storage photon generators 270 b may beoptically coupled to the first end 226 b of the second dopedpolycrystalline ceramic optical device 220 b. The one or more storagephoton generators 270 a, 270 b may comprise any of the storage photongenerators 170 described above.

Further, the one or more pump lasers 280 are optically coupled to thedoped polycrystalline ceramic optical devices 220 a, 220 b. For example,the one or more pump lasers 280 may comprise a first pump laser 280 aand a second pump laser 280 b each optically coupled to the first dopedpolycrystalline ceramic optical device 220 a as well as a third pumplaser 280 c and a fourth pump laser 280 d each optically coupled to thesecond doped polycrystalline ceramic optical device 220 b. For example,as depicted in FIG. 3, the first pump laser 280 a may be opticallycoupled to the first end 226 a of the first doped polycrystallineceramic optical device 220 a, the second pump laser 280 b may beoptically coupled to the second end 228 a of the first dopedpolycrystalline ceramic optical device 220 a, the third pump laser 280 cmay be optically coupled to the first end 226 b of the second dopedpolycrystalline ceramic optical device 220 b, and the fourth pump laser280 d may be optically coupled to the second end 228 b of the seconddoped polycrystalline ceramic optical device 220 b. Moreover, the one ormore pump lasers 280 may comprise any of the pump lasers 180 describedabove.

Further, the one or more storage photon generators 270 a, 270 b, the oneor more pump lasers 280 a, 280 b and/or the doped polycrystallineceramic optical devices 220 a, 220 b may be coupled to one or morealignment mechanisms 242 to optically align the one or more storagephoton generators 270 a, 270 b and the one or more pump lasers 280 withthe doped polycrystalline ceramic optical devices 220 a, 220 b. Further,the one or more alignment mechanisms 242 may comprise any of thealignment mechanisms 142 described above. Moreover, the dopedpolycrystalline ceramic optical devices 220 a, 220 b doped with therare-earth element dopants 230 a, 230 b are configured to absorb andrelease storage photons as described above with respect to FIGS. 1 and2.

The optical system 200 may further comprise first and second WDMs 260 a,260 b, optically coupled to the first and second doped polycrystallineceramic optical devices 220 a, 220 b, for example, the respective firstends 226 a, 226 b of the first and second doped polycrystalline ceramicoptical devices 220 a, 220 b. The WDMs 260 a, 260 b may each comprisethe WDM 160 described above. Further, WDMs 260 a, 260 b may be opticallycoupled to both storage photon pathways 262 a, 262 b and pump pulsepathways 264 a, 264 b for example, the WDMs 260 a, 260 b may bepositioned between the first ends 226 a, 226 b of the first and seconddoped polycrystalline ceramic optical devices 220 a, 220 b and both thestorage photon pathways 262 a, 262 b and the pump pulse pathways 264 a,264 b.

The storage photon pathways 262 a, 262 b may extend between the WDMs 260a, 260 b and the repeater entanglement optics 210. For example, thefirst storage photon pathway 262 a may extend between and opticallycouple the first WDM 260 a and a first entangling pathway 212 a of therepeater entanglement optics 210. Further, the second storage photonpathway 262 b may extend between and optically couple the second WDM 260b and a second entangling pathway 212 b of the repeater entanglementoptics 210. Moreover, the pump pulse pathways 264 a, 264 b may extendbetween the WDMs 260 a, 260 b and pump pulse receivers 268 a, 268 b,which may comprise the pump pulse receiver 168, described above.

As depicted in FIG. 4, the optical system 200 may further comprise firstand second optical circulators 250 a, 250 b, positioned adjacent andoptically coupled to the respective first and second dopedpolycrystalline ceramic optical devices 220 a, 220 b, for example, tothe respective first ends 226 a, 226 b of the first and second dopedpolycrystalline ceramic optical devices 220 a, 220 b, as depicted inFIG. 4. The first and second optical circulators 250 a, 250 b maycomprise any of the optical circulators 150 described above. Forexample, the first and second optical circulators 250 a, 250 b may eachcomprise three or more optical ports, for example, a first optical port252 a, 252 b, a second optical port 254 a, 254 b, and a third opticalport 256 a, 256 b.

The first and second optical circulators 250 a, 250 b are positionedbetween the respective first and second storage photon generators 270 aand first and second doped polycrystalline ceramic optical devices 220a, 220 b. For example, the first optical ports 252 a, 252 b of the firstand second optical circulators 250 a, 250 b are optically coupled to therespective first and second storage photon generators 270 a, 270 b andthe second optical ports 254 a, 254 b of the first and second opticalcirculators 250 a, 250 b are optically coupled to the respective firstends 226 a, 226 b of the first and second doped polycrystalline ceramicoptical devices 220 a, 220 b.

Further, the first optical circulator 250 a may also be positionedbetween at least one of the pump lasers 280 (e.g., the first pump laser280 a) and the first doped polycrystalline ceramic optical device 220 a,for example, the first end 226 a of the first doped polycrystallineceramic optical device 220 a such that the first optical port 252 a ofthe first optical circulator 250 a is optically coupled to at least oneof the one or more pump lasers 280 (e.g., the first pump laser 280 a)and the second optical port 254 a of the first optical circulator 250 ais optically coupled to the first end 226 a of the first dopedpolycrystalline ceramic optical device 220 a. For example, as depictedin FIG. 4, the first storage photon generator 270 a and the first pumplaser 280 a are each optically coupled to the first optical port 252 aof the first optical circulator 250 a such that storage photons outputby the first storage photon generator 270 a and the pump pulse output bythe first pump laser 180 a enter the first optical port 252 a of thefirst optical circulator 250 a and exit the second optical port 254 atowards the first end 226 a of the first doped polycrystalline ceramicoptical device 220 a.

Moreover, the second optical circulator 250 b may also be positionedbetween at least one of the pump lasers 280 (e.g., the third pump laser280 c) and the second doped polycrystalline ceramic optical device 220b, for example, the first end 226 b of the second doped polycrystallineceramic optical device 220 b such that the first optical port 252 b ofthe second optical circulator 250 b is optically coupled to at least oneof the one or more pump lasers 280 (e.g., the third pump laser 280 c)and the second optical port 254 b of the second optical circulator 250 bis optically coupled to the first end 226 b of the second dopedpolycrystalline ceramic optical device 220 b. For example, as depictedin FIG. 4, the second storage photon generator 270 b and the third pumplaser 280 c are each optically coupled to the first optical port 252 bof the second optical circulator 250 b such that storage photons outputby the second storage photon generator 270 b and the pump pulse outputby the third pump laser 280 c enter the first optical port 252 b of thesecond optical circulator 250 b and exit the second optical port 254 btowards the first end 226 b of the second doped polycrystalline ceramicoptical device 220 b.

The first and second optical circulators 250 a, 250 b may also bepositioned between the respective first and second WDMs 260 a, 260 b andthe first and second doped polycrystalline ceramic optical devices 220a, 220 b, for example, the respective first ends 226 a, 226 b of thefirst and second doped polycrystalline ceramic optical devices 220 a,220 b. Further, the third optical port 256 a, 256 b of the first andsecond optical circulators 250 a, 250 b are optically coupled to therespective first and second WDMs 260 a, 260 b such that the first andsecond WDMs 260 a, 260 b receive the storage photon after the storagephoton exits the first end 226 a, 226 b of the first and second dopedpolycrystalline ceramic optical devices 220 a, 220 b and may receivesome or all of the pump pulses output by the first, second, third, andfourth pump lasers 280 a, 280 b, 280 c, 280 d.

Referring still to FIG. 4, the repeater entanglement optics 210 of thequantum repeater system 201 each comprise two entangling pathways 212 a,212 b optically coupled to and the second ends 228 a, 228 b of eachdoped polycrystalline ceramic optical devices 220 a, 220 b, for example,using the first and second WDMs 260 a, 260 b and the first and secondstorage photon pathways 262 a, 262 b. The two entangling pathways 212 a,212 b may also be optically coupled to two entanglement detectors 214 a,214 b. The repeater entanglement optics 210 further comprise abeamsplitter 216 positioned such that each entangling pathway 212 a, 212b traverses the beamsplitter 216. Further the two entanglement detectors214 a, 214 b may each comprise one or more single-photon detectors,e.g., superconducting nanowire single-photon detectors, low noisephotodiodes, or the like. In operation, the repeater entanglement optics210 are structurally configured to entangle pairs of storage photonswhen storage photons output by each doped polycrystalline ceramicoptical device 220 a, 220 b simultaneously traverse the beamsplitter216.

In operation, each doped polycrystalline ceramic optical device 220 a,220 b doped with the rare-earth element dopant 230 a, 230 b isstructurally and compositionally configured to absorb and storeindividual storage photons emitted by the storage photon generators 270a, 270 b. For example, when a shaped spectral structure has beengenerated in the rare-earth element dopant 230 of each dopedpolycrystalline ceramic optical device 220 a, 220 b and the storagephotons are traversing each doped polycrystalline ceramic optical device220 a, 220 b, each storage photons may each transfer a superposition ofthe shaped spectral structure of the rare-earth element dopants 230 a,230 b from the first split ground state G₁ to the excited energy stateE₁, as schematically shown in FIG. 2, to absorb each respective storagephoton in each respective doped polycrystalline ceramic optical device220 a, 220 b. Further, upon receipt of a first pump pulse output by thefirst and second pump lasers 280 a, 280 b, each first pump pulse maytransfer the superposition of the shaped spectral structure of therare-earth element dopant 230 a, 230 b of each respective dopedpolycrystalline ceramic optical device 220 a, 220 b from the excitedenergy state E₁ into the second split ground state G₂, to store eachstorage photon.

Each doped polycrystalline ceramic optical device 220 a, 220 b dopedwith the rare-earth element dopant 230 a, 230 b is also structurally andcompositionally configured to release, on demand, the storage photonstored within each doped polycrystalline ceramic optical device 220 a,220 b. For example, upon receipt of a second pump pulse output by thethird and fourth pump lasers 280 a, 280 b, the superposition of theshaped spectral structure of the rare-earth element dopants 230 a, 230 bis transferred from the second split ground state G₂ back to the excitedenergy state E₁. Once in the excited energy state E₁, the shapedspectral structure of the rare-earth element dopants 230 a, 230 b willautomatically release the storage photons after a delay period, suchthat the storage photons exit each doped polycrystalline ceramic opticaldevice 220 a, 220 b, for example, the first ends 226 a, 226 b of eachdoped polycrystalline ceramic optical device 220 a, 220 b.

Further, if the third and fourth pump lasers 280 c, 280 d emit secondpump pulses that are simultaneously received by the first and seconddoped polycrystalline ceramic optical devices 220 a, 220 b (e.g., byemitting the second pump pulses simultaneously), the first and seconddoped polycrystalline ceramic optical devices 220 a, 220 b willsimultaneously release the storage photons (after the delay period),allowing the storage photons to simultaneously traverse the beamsplitter216 of the repeater entanglement optics 210, entangling the storagephotons. Moreover, because doped polycrystalline ceramic optical devices220 a, 220 b comprise long photon storage lifetimes, one dopedpolycrystalline ceramic optical device 220 a/220 b may absorb and storea first storage photon before the other doped polycrystalline ceramicoptical device 220 a/220 b absorbs and stores a second storage photon,allowing storage photons that are not simultaneously received by thedoped polycrystalline ceramic optical device 220 a, 220 b to besimultaneously released by the doped polycrystalline ceramic opticaldevice 220 a, 220 b and entangled by the repeater entanglement optics210.

Referring now to FIG. 5, the optical system 200 may be arranged as anentangled photon generator 301 structurally configured to generate fouror more entangled photons, for example, two or more entangled pairs ofphotons. Further, the optical system 200 may be positioned in one ormore photon entanglement chains of a quantum key generation system, forexample, the quantum key generation systems described in U.S. patentapplication Ser. No. 14/680,522. As depicted in FIG. 5, the opticalsystem 200 arranged as the entangled photon generator 301 comprises afirst quantum repeater system 310 a, a second quantum repeater system310 b, a repeater coupling entanglement optics 370, a pathway splitter375, and an entanglement detector 372. Further, the first and secondquantum repeater system 310 a, 310 b may comprise any of the quantumrepeater systems 201 described above with respect to FIG. 4.

In some embodiments, the first and second quantum repeater systems 310a, 310 b may comprise entanglement optics (e.g., the repeaterentanglement optics 210 of FIG. 4, above) that do not include twoentanglement detectors 214 a, 214 b such that each entangling pathway212 a, 212 b may be optically coupled to the repeater couplingentanglement optics 370 of the entangled photon generator 301. In otherembodiments, the first and second quantum repeater systems 310 a, 310 bmay include the entanglement detectors 214 a, 214 b and the repeatercoupling entanglement optics 370 of the entangled photon generator 301may be optically coupled to each entangling pathway 212 a, 212 b, forexample, when the entanglement detectors 214 a, 214 b are structurallyconfigured to detect the storage photons without the storage photonsterminating therein.

Referring still to FIG. 5, the repeater coupling entanglement optics 370may comprise a first entangling pathway 371 a optically coupled to andextending between the first quantum repeater system 310 a and theentanglement detector 372 and a second entangling pathway 371 boptically coupled to and extending between the second quantum repeatersystem 310 b and the pathway splitter 375. Additional entanglingpathways 371 are contemplated in embodiments comprising additionalquantum repeater systems 310. In some embodiments, the repeater couplingentanglement optics 370 further comprise a beamsplitter 373 positionedsuch that each entangling pathway 371 a, 371 b traverses thebeamsplitter 373. In operation, the repeater coupling entanglementoptics 370 are structurally configured to entangle multiple photons(e.g., storage photons) when the multiple photons simultaneouslytraverse the beamsplitter 373. For example, when each entangled pair ofphotons output by the first and second quantum repeater systems 310 a,310 b simultaneously traverse the beamsplitter 373, all four photons areentangled with each other.

Further, the repeater coupling entanglement optics 370 are configuredsuch that some or all of the entangled photons output by each of thefirst and second quantum repeater systems 310 a, 310 b are received bythe entanglement detector 372 and/or the pathway splitter 375. Forexample, when a first entangled pair of photons are output by the firstquantum repeater system 310 a and a second entangled pair of photons areoutput by the second quantum repeater system 310 b and these twoentangled pairs of photons are entangled with each other at thebeamsplitter 373, there is a probability that one of at least threeoutcomes occur, which are mathematically described by the wave function:

$\left. \Psi \right\rangle_{{AA}^{\prime}} = {- {\left\lbrack {{\frac{1}{2}\left. {2,2} \right\rangle} + {\sqrt{\frac{3}{8}}\left( {\left. {4,0} \right\rangle + \left. {0,4} \right\rangle} \right)}} \right\rbrack.}}$In a first outcome, both the entanglement detector 372 and the pathwaysplitter 375 receive two of the four entangled photons, mathematicallydescribed by the ket |2,2

in the above wave function. In a second outcome, the entanglementdetector 372 receives the four entangled photons, mathematicallydescribed by one of the kets |4,0

or |4,0

in the above wave function. In a third outcome, the pathway splitter 375receives the four entangled photons, mathematically described by one ofthe kets |4,0

or |4,0

in the above wave function. In some embodiments, the probability thatthe pathway splitter 375 receives the four entangled photons is about ⅜.Further, embodiments comprising additional parametric down conversiongenerators are contemplated such that additional entangled pairs ofphotons (e.g., N entangled photons) may be entangled by the repeatercoupling entanglement optics 370. In an embodiment comprising Nentangled photons, the probability that the N entangled photons arereceived by the entanglement detector 372, the pathway splitter 375, ora combination of both is mathematically described by the generalizedket:

$\left. {N,N} \right\rangle_{out} = {\frac{i^{N}}{{N!}2^{N}}{\sum\limits_{p = 0}^{N}\;{\begin{pmatrix}N \\p\end{pmatrix}\sqrt{{\left( {2p} \right)!}{\left( {{2N} - {2p}} \right)!}}{\left. {{2p},{{2N} - {2p}}} \right\rangle.}}}}$

Further, in some embodiments, at least a portion of both the first andsecond entangling pathways 371 a, 371 b may comprise multicore opticalfibers. For example, a portion of the first entangling pathway 371 athat extends between the beamsplitter 373 and the pathway splitter 375and a portion of the second entangling pathway 371 b that extendsbetween the beamsplitter 373 and the pathway splitter 375 may eachcomprise multicore optical fiber. In some embodiments, at least aportion of both the first and second entangling pathways 371 a, 371 bmay comprise one or more optical waveguides.

In some embodiments, the pathway splitter 375 is structurally configuredto direct entangled pairs of photons into optical fiber links 360optically coupled to the pathway splitter 375. For example, when thepathway splitter 375 receives four entangled photons, the pathwaysplitter 375 may direct two of the four entangled photons into oneoptical fiber link 360 and the pathway splitter 375 may direct two ofthe four entangled photons into another optical fiber link 360. Theoptical fiber links 360 may comprise any optical fiber, for example, aglass optical fiber comprising a single core or comprising multiplecores. Further, in embodiments when the entangled photon generator 301is configured to generate more than four entangled photons, the pathwaysplitter 375 may direct a first subset (e.g., about half) of theentangled photons into one optical fiber link 360 (e.g., a first opticalfiber link) and the pathway splitter 375 may also direct a second subset(e.g., about half) of the entangled photons into another optical fiberlink 360 (e.g., a second optical fiber link). In some embodiments, thepathway splitter 375 may comprise a fused biconical taper splitter, aplanar lightwave circuit splitter, or the like.

In some embodiments, the entanglement detector 372 is structurallyconfigured to measure the number of photons received by the entanglementdetector 372, which also provides information regarding the number ofphotons received by the pathway splitter 375. For example, if twoentangled photons are output by each of the first and second quantumrepeater systems 310 a, 310 b and zero entangled photons are received bythe entanglement detector 372, than all four entangled photons arereceived by the pathway splitter 375. In some embodiments, theentanglement detector 372 may comprise a multi-photon detector. Inalternative embodiments, the entanglement detector 372 may comprise asingle-photon detector, e.g., a superconducting nanowire single-photondetector, a low noise photodiode, or the like.

It is noted that recitations herein of a component of the presentdisclosure being “configured” in a particular way, to embody aparticular property, or to function in a particular manner, arestructural recitations, as opposed to recitations of intended use. Morespecifically, the references herein to the manner in which a componentis “configured” denotes an existing physical condition of the componentand, as such, is to be taken as a definite recitation of the structuralcharacteristics of the component.

For the purposes of describing and defining the present invention it isnoted that the term “about” is utilized herein to represent the inherentdegree of uncertainty that may be attributed to any quantitativecomparison, value, measurement, or other representation. The term“about” is also utilized herein to represent the degree by which aquantitative representation may vary from a stated reference withoutresulting in a change in the basic function of the subject matter atissue.

Having described the subject matter of the present disclosure in detailand by reference to specific embodiments thereof, it is noted that thevarious details disclosed herein should not be taken to imply that thesedetails relate to elements that are essential components of the variousembodiments described herein, even in cases where a particular elementis illustrated in each of the drawings that accompany the presentdescription. Further, it will be apparent that modifications andvariations are possible without departing from the scope of the presentdisclosure, including, but not limited to, embodiments defined in theappended claims. More specifically, although some aspects of the presentdisclosure are identified herein as preferred or particularlyadvantageous, it is contemplated that the present disclosure is notnecessarily limited to these aspects.

It is noted that one or more of the following claims utilize the term“wherein” as a transitional phrase. For the purposes of defining thepresent invention, it is noted that this term is introduced in theclaims as an open-ended transitional phrase that is used to introduce arecitation of a series of characteristics of the structure and should beinterpreted in like manner as the more commonly used open-ended preambleterm “comprising.”

What is claimed is:
 1. A quantum memory system comprising a dopedpolycrystalline ceramic, a magnetic field generation unit, a storagephoton generator, and one or more pump lasers, wherein: the dopedpolycrystalline ceramic is positioned within a magnetic field of themagnetic field generation unit when the magnetic field generation unitgenerates the magnetic field; the one or more pump lasers are opticallycoupled to the doped polycrystalline ceramic; the storage photongenerator is optically coupled to the doped polycrystalline ceramic andis structurally configured to output an entangled pair of storagephotons comprising a first entangled storage photon entangled with asecond entangled storage photon; and the doped polycrystalline ceramicis doped with a rare-earth element dopant that is uniformly distributedwithin a crystal lattice of the doped polycrystalline ceramic andcomprises about 0.01% to about 2% of a total molecular weight of thedoped polycrystalline ceramic, wherein: the one or more pump lasers areconfigured to irradiate the doped polycrystalline ceramic and generate ashaped spectral structure within the rare-earth element dopant of thedoped polycrystalline ceramic; the rare-earth element dopant isconfigured to absorb a storage photon traversing the dopedpolycrystalline ceramic when (i) the storage photon transfers asuperposition of the shaped spectral structure of the rare-earth elementdopant from a first split ground state to an excited energy state and(ii), upon receipt of a first pump pulse output by the one or more pumplasers, the first pump pulse transfers the superposition of the shapedspectral structure of the rare-earth element dopant from the excitedenergy state into a second split ground state; and the rare-earthelement dopant is configured to release the storage photon when (i) thesuperposition of the shaped spectral structure of the rare-earth elementdopant is transferred from the second split ground state to the excitedenergy state, upon receipt of a second pump pulse output by the one ormore pump lasers and (ii) the superposition of the shaped spectralstructure of the rare-earth element dopant automatically releases thestorage photon after a delay period such that the storage photon exitsthe doped polycrystalline ceramic.
 2. The quantum memory system of claim1, wherein the doped polycrystalline ceramic comprises yttrium oxide,zirconium oxide, or combinations thereof.
 3. The quantum memory systemof claim 1, wherein the doped polycrystalline ceramic is voidless.
 4. Aquantum memory system comprising a doped polycrystalline ceramic, amagnetic field generation unit, a storage photon generator, and one ormore pump lasers, wherein: the doped polycrystalline ceramic ispositioned within a magnetic field of the magnetic field generation unitwhen the magnetic field generation unit generates the magnetic field;the one or more pump lasers are optically coupled to the dopedpolycrystalline ceramic; the storage photon generator is opticallycoupled to the doped polycrystalline ceramic and is structurallyconfigured to output an entangled pair of storage photons comprising afirst entangled storage photon entangled with a second entangled storagephoton; and the doped polycrystalline ceramic is doped with a rare-earthelement dopant that is uniformly distributed within a crystal lattice ofthe doped polycrystalline ceramic and comprises about 0.01% to about 2%of a total molecular weight of the doped polycrystalline ceramic,wherein the doped polycrystalline ceramic is a core of a waveguide, thequantum memory system further comprising a cladding surrounding thecore.
 5. The quantum memory system of claim 4, wherein the corecomprises yttrium oxide, zirconium oxide, or combinations thereof andthe cladding comprises yttrium oxide or polymer.
 6. The quantum memorysystem of claim 4, wherein the rare-earth element dopant compriseserbium, thulium, praseodymium, or a combination thereof.
 7. A quantummemory system comprising a doped polycrystalline ceramic, a magneticfield generation unit, a storage photon generator, and one or more pumplasers, wherein: the doped polycrystalline ceramic is positioned withina magnetic field of the magnetic field generation unit when the magneticfield generation unit generates the magnetic field; the one or more pumplasers are optically coupled to the doped polycrystalline ceramic; thestorage photon generator is optically coupled to the dopedpolycrystalline ceramic and is structurally configured to output anentangled pair of storage photons comprising a first entangled storagephoton entangled with a second entangled storage photon; and the dopedpolycrystalline ceramic is doped with a rare-earth element dopant thatis uniformly distributed within a crystal lattice of the dopedpolycrystalline ceramic and comprises about 0.01% to about 2% of a totalmolecular weight of the doped polycrystalline ceramic, wherein therare-earth element dopant comprises between about 0.05% to about 0.15%of a total molecular weight of the doped polycrystalline ceramic.
 8. Aquantum memory system comprising a doped polycrystalline ceramic, amagnetic field generation unit, a storage photon generator, and one ormore pump lasers, wherein: the doped polycrystalline ceramic ispositioned within a magnetic field of the magnetic field generation unitwhen the magnetic field generation unit generates the magnetic field;the one or more pump lasers are optically coupled to the dopedpolycrystalline ceramic; the storage photon generator is opticallycoupled to the doped polycrystalline ceramic and is structurallyconfigured to output an entangled pair of storage photons comprising afirst entangled storage photon entangled with a second entangled storagephoton; and the doped polycrystalline ceramic is doped with a rare-earthelement dopant that is uniformly distributed within a crystal lattice ofthe doped polycrystalline ceramic and comprises about 0.01% to about 2%of a total molecular weight of the doped polycrystalline ceramic,further comprising an optical circulator optically coupled to a firstend of the doped polycrystalline ceramic, wherein the optical circulatorcomprises a first optical port, a second optical port, and a thirdoptical port.
 9. The quantum memory system of claim 8, wherein: theoptical circulator is positioned between the storage photon generatorand the first end of the doped polycrystalline ceramic such that thefirst optical port of the optical circulator is optically coupled to thestorage photon generator and the second optical port is opticallycoupled to the first end of the doped polycrystalline ceramic; and theoptical circulator positioned between at least one of the one or morepump lasers and the first end of the doped polycrystalline ceramic suchthat the first optical port of the optical circulator is opticallycoupled to at least one of the one or more pump lasers and the secondoptical port is optically coupled to the first end of the dopedpolycrystalline ceramic.
 10. The quantum memory system of claim 8,wherein the third optical port of the optical circulator is opticallycoupled to a wavelength division multiplexer.
 11. A quantum memorysystem comprising a doped polycrystalline ceramic, a magnetic fieldgeneration unit, a storage photon generator, and one or more pumplasers, wherein: the doped polycrystalline ceramic is positioned withina magnetic field of the magnetic field generation unit when the magneticfield generation unit generates the magnetic field; the one or more pumplasers are optically coupled to the doped polycrystalline ceramic; thestorage photon generator is optically coupled to the dopedpolycrystalline ceramic and is structurally configured to output anentangled pair of storage photons comprising a first entangled storagephoton entangled with a second entangled storage photon; and the dopedpolycrystalline ceramic is doped with a rare-earth element dopant thatis uniformly distributed within a crystal lattice of the dopedpolycrystalline ceramic and comprises about 0.01% to about 2% of a totalmolecular weight of the doped polycrystalline ceramic, wherein the oneor more pump lasers comprise a first pump laser optically coupled to afirst end of the doped polycrystalline ceramic and a second pump laseroptically coupled to a second end of the doped polycrystalline ceramic.12. A quantum memory system comprising a doped polycrystalline ceramic,a magnetic field generation unit, a storage photon generator, and one ormore pump lasers, wherein: the doped polycrystalline ceramic ispositioned within a magnetic field of the magnetic field generation unitwhen the magnetic field generation unit generates the magnetic field;the one or more pump lasers are optically coupled to the dopedpolycrystalline ceramic; the storage photon generator is opticallycoupled to the doped polycrystalline ceramic and is structurallyconfigured to output an entangled pair of storage photons comprising afirst entangled storage photon entangled with a second entangled storagephoton; and the doped polycrystalline ceramic is doped with a rare-earthelement dopant that is uniformly distributed within a crystal lattice ofthe doped polycrystalline ceramic and comprises about 0.01% to about 2%of a total molecular weight of the doped polycrystalline ceramic,wherein: the one or more pump lasers are structurally configured togenerate a first pump photon comprising a first pump photon wavelengthand a second pump photon comprising a second pump photon wavelength; andthe first pump photon wavelength and the second pump photon wavelengthare each within about 20 nm of an absorption peak of the dopedpolycrystalline ceramic doped with the rare-earth element dopant.
 13. Aquantum memory system comprising a doped polycrystalline ceramic, amagnetic field generation unit, a storage photon generator, and one ormore pump lasers, wherein: the doped polycrystalline ceramic ispositioned within a magnetic field of the magnetic field generation unitwhen the magnetic field generation unit generates the magnetic field;the one or more pump lasers are optically coupled to the dopedpolycrystalline ceramic; the storage photon generator is opticallycoupled to the doped pplycrystalline ceramic and is structurallyconfigured to output an entangled pair of storage photons comprising afirst entangled storage photon entangled with a second entangled storagephoton; and the doped polycrystalline ceramic is doped with a rare-earthelement dopant that is uniformly distributed within a crystal lattice ofthe doped polycrystalline ceramic and comprises about 0.01% to about 2%of a total molecular weight of the doped polycrystalline ceramic,further comprising a cooling system thermally coupled to the dopedpolycrystalline ceramic.
 14. An optical system comprising a quantumrepeater system, one or more magnetic field generation units, one ormore storage photon generators, and one or more pump lasers, wherein:the quantum repeater system comprises two doped polycrystalline ceramicsand repeater entanglement optics; each doped polycrystalline ceramic ofthe quantum repeater system is positioned within a magnetic field of theone or more magnetic field generation units when the one or moremagnetic field generation units generate the magnetic field; each dopedpolycrystalline ceramic of the quantum repeater system is doped with arare-earth element dopant that is uniformly distributed within a crystallattice of the doped polycrystalline ceramic and comprises about 0.01%to about 2% of a total molecular weight of the doped polycrystallineceramic; each doped polycrystalline ceramic is optically coupled to atleast one of the one or more the storage photon generators, which arestructurally configured to output an entangled pair of storage photonscomprising a first entangled storage photon entangled with a secondentangled storage photon; and each doped polycrystalline ceramic isoptically coupled to at least one of the one or more pump lasers; andthe repeater entanglement optics comprise two entangling pathwaysoptically coupled to each doped polycrystalline ceramic and abeamsplitter positioned such that each entangling pathway traverses thebeamsplitter.
 15. The optical system of claim 14, wherein: the repeaterentanglement optics further comprise two entanglement detectorsoptically coupled to the two entangling pathways; and the repeaterentanglement optics are structurally configured to entangle pairs ofstorage photons when storage photons output by each dopedpolycrystalline ceramic simultaneously traverse the beamsplitter. 16.The optical system of claim 14, wherein: the quantum repeater system isa first quantum repeater system and the optical system further comprisesa second quantum repeater system, repeater entanglement optics, apathway splitter, and an entanglement detector; the second quantumrepeater system comprises two doped polycrystalline ceramics andrepeater entanglement optics; each doped polycrystalline ceramic of thesecond quantum repeater system is positioned within a magnetic field ofthe one or more magnetic field generation units when the one or moremagnetic field generation units generate the magnetic field; and therepeater entanglement optics comprise a first entangling pathwayoptically coupled to and extending between the first quantum repeatersystem and the entanglement detector and a second entangling pathwayoptically coupled to and extending between the second quantum repeatersystem and the pathway splitter.
 17. The optical system of claim 16,wherein: the repeater entanglement optics further comprise abeamsplitter positioned such that each entangling pathway traverses thebeamsplitter; and the repeater entanglement optics are structurallyconfigured to entangle entangled pairs of photons output by the firstand second quantum repeater systems when each entangled pair of photonsoutput by the first and second quantum repeater systems simultaneouslytraverse the beamsplitter.
 18. A quantum memory system comprising adoped polycrystalline ceramic, a magnetic field generation unit, astorage photon generator, and one or more pump lasers, wherein: thedoped polycrystalline ceramic is positioned within a magnetic field ofthe magnetic field generation unit when the magnetic field generationunit generates the magnetic field; the one or more pump lasers areoptically coupled to the doped polycrystalline ceramic; the storagephoton generator is optically coupled to the doped polycrystallineceramic and is structurally configured to output entangled pairs ofstorage photons comprising a first entangled storage photon entangledwith a second entangled storage photon; and the doped polycrystallineceramic is doped with a rare-earth element dopant that is configured toabsorb about 70% or more of storage photons that propagate into thedoped polycrystalline ceramic and store an absorbed storage photon for aphoton storage lifetime of from about 1 μs to about 1 ms and isconfigured such that a plurality of storage photons traversing the dopedpolycrystalline ceramic attenuate at an attenuation rate of about 2dB/mm or less.
 19. The quantum memory system of claim 18, wherein therare-earth element dopant doped into the doped polycrystalline ceramicis configured to absorb about 90% or more of storage photons thatpropagate into the doped polycrystalline ceramic and store an absorbedstorage photon for a photon storage lifetime of from about 10 μs toabout 1 ms and is configured such that a plurality of storage photonstraversing the doped polycrystalline ceramic attenuate at an attenuationrate of about 1 dB/mm or less.